Datasets:
christopher
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oeis

Dataset card Data Studio Files
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Community
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348
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timestamp[us]date
1999-12-11 03:00:00
2025-04-25 01:21:50
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A360201
Number of induced paths in the n-ladder graph P_2 X P_n.
[ "1", "8", "25", "58", "117", "218", "387", "666", "1123", "1868", "3079", "5044", "8229", "13388", "21741", "35262", "57145", "92558", "149863", "242590", "392631", "635408", "1028235", "1663848", "2692297", "4356368", "7048897", "11405506", "18454653", "29860418", "48315339", "78176034", "126491659", "204667988" ]
[ "nonn", "easy" ]
10
0
5
[ "A360199", "A360201" ]
null
Andrew Howroyd, Jan 29 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360201.seq
f2f875700411ce31ca1c2b682073f7c7
A360202
Array read by antidiagonals: T(m,n) is the number of (non-null) induced trees in the grid graph P_m X P_n.
[ "1", "3", "3", "6", "12", "6", "10", "33", "33", "10", "15", "78", "138", "78", "15", "21", "171", "533", "533", "171", "21", "28", "360", "2003", "3568", "2003", "360", "28", "36", "741", "7453", "23686", "23686", "7453", "741", "36", "45", "1506", "27643", "156614", "277606", "156614", "27643", "1506", "45", "55", "3039", "102432", "1034875", "3234373", "3234373", "1034875", "102432", "3039", "55" ]
[ "nonn", "tabl" ]
12
0
5
[ "A000217", "A116469", "A125128", "A287151", "A360196", "A360199", "A360202", "A360203", "A360918" ]
null
Andrew Howroyd, Feb 22 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360202.seq
574553dbbda2bc62d5410a67a04bece9
A360203
Number of (non-null) induced trees in the n X n grid graph.
[ "1", "12", "138", "3568", "277606", "66136452", "48136454388", "106601739449932", "716581962133166734", "14594259085593605592840", "899530518959027898354960664", "167638624754374503965030664785872", "94397539071875018677962029008899452442", "160524233982090828046095750880433748533447560" ]
[ "nonn" ]
6
0
5
[ "A059525", "A080691", "A297664", "A360200", "A360202", "A360203" ]
null
Andrew Howroyd, Feb 22 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360203.seq
64509047a2d7159441deac9037978d2c
A360204
Primitive prime powers. p is a primitive prime power iff it is an odd prime power that exceeds the preceding odd prime power by more than any smaller odd prime power does. ('Prime power' defined in the sense of A246655.)
[ "5", "17", "37", "97", "149", "211", "307", "907", "1151", "1361", "5623", "8501", "9587", "15727", "19661", "31469", "156007", "360749", "370373", "492227", "1349651", "1357333", "2010881", "4652507", "17051887", "20831533", "47326913", "122164969", "189695893", "191913031", "387096383", "436273291", "1294268779" ]
[ "nonn" ]
25
0
5
[ "A061345", "A246655", "A360204" ]
null
Peter Luschny, Feb 01 2023
2023-02-02T06:48:53
oeisdata/seq/A360/A360204.seq
a9483b11a3094d00983e829668feee1f
A360205
Triangle read by rows. T(n, k) = (-1)^(n-k)*(k+1)*binomial(n, k)*pochhammer(1-n, n-k).
[ "1", "0", "2", "0", "4", "3", "0", "12", "18", "4", "0", "48", "108", "48", "5", "0", "240", "720", "480", "100", "6", "0", "1440", "5400", "4800", "1500", "180", "7", "0", "10080", "45360", "50400", "21000", "3780", "294", "8", "0", "80640", "423360", "564480", "294000", "70560", "8232", "448", "9", "0", "725760", "4354560", "6773760", "4233600", "1270080", "197568", "16128", "648", "10" ]
[ "nonn", "tabl" ]
6
0
5
[ "A002720", "A045991", "A052849", "A069138", "A271703", "A360174", "A360205" ]
null
Peter Luschny, Feb 08 2023
2023-02-08T18:11:10
oeisdata/seq/A360/A360205.seq
328446667967108e51ad6635bd074a7a
A360206
Triangular array T(m,n) read by antidiagonals: T(m,n) = prime(m+n) - prime(m) - prime(n).
[ "-1", "0", "1", "0", "3", "3", "2", "3", "5", "5", "0", "3", "3", "5", "7", "2", "3", "5", "9", "7", "11", "0", "3", "7", "7", "9", "11", "9", "2", "7", "7", "11", "11", "11", "11", "15", "4", "5", "9", "11", "9", "11", "13", "17", "15", "0", "5", "7", "7", "7", "11", "13", "13", "15", "13", "4", "7", "7", "9", "11", "15", "13", "17", "17", "13", "17", "2", "3", "5", "9", "11", "11", "13", "15", "13", "13" ]
[ "tabl", "sign" ]
15
0
5
[ "A000040", "A066066", "A360206" ]
null
Clark Kimberling, Jan 30 2023
2023-02-01T08:17:08
oeisdata/seq/A360/A360206.seq
998b23adc05001631587eaf751d49997
A360207
Triangular array T(n,k) read by antidiagonals: T(2,1) = 1; otherwise T(n,k) = p(n)!/(p(k)!*p(n-k)!), where p(0)=1 and p(m)=prime(m) for m > 0.
[ "1", "1", "1", "1", "1", "1", "1", "10", "10", "1", "1", "21", "140", "21", "1", "1", "3960", "55440", "55440", "3960", "1", "1", "78", "205920", "432432", "205920", "78", "1", "1", "28560", "1485120", "588107520", "588107520", "1485120", "28560", "1", "1", "171", "3255840", "25395552", "4788875520", "25395552", "3255840", "171", "1" ]
[ "nonn", "tabl" ]
16
0
5
[ "A007318", "A008578", "A360207", "A360208" ]
null
Clark Kimberling, Jan 30 2023
2023-02-02T16:52:32
oeisdata/seq/A360/A360207.seq
d3e70ec910fd5fb61c6aeddb5dc9b118
A360208
Triangular array T(n,k) read by antidiagonals T(n,k) = F(n)!/(F(k)!*F(n-k)!), where F(m) = A000045(m) = m-th Fibonacci number.
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "3", "6", "3", "1", "1", "20", "60", "60", "20", "1", "1", "336", "6720", "10080", "6720", "336", "1", "1", "154440", "51891840", "518918400", "518918400", "51891840", "154440", "1", "1", "8204716800", "1267136462592000", "212878925715456000", "1419192838103040000", "212878925715456000", "1267136462592000", "8204716800", "1" ]
[ "nonn", "tabl" ]
18
0
5
[ "A000045", "A007318", "A360207", "A360208" ]
null
Clark Kimberling, Jan 30 2023
2024-06-22T14:13:39
oeisdata/seq/A360/A360208.seq
1660b5aea5a7bc5a19e2d467d0321cda
A360209
Lexicographically earliest infinite sequence of distinct positive numbers such that, for n > 2, a(n) shares a factor with a(n-2) + a(n-1) but shares no factor with a(n-2).
[ "1", "2", "3", "5", "4", "6", "15", "7", "8", "9", "17", "10", "12", "11", "23", "14", "37", "27", "16", "43", "59", "18", "21", "13", "20", "22", "33", "25", "26", "24", "35", "295", "32", "36", "51", "29", "28", "19", "47", "30", "44", "259", "39", "34", "73", "107", "38", "40", "45", "119", "41", "46", "42", "55", "97", "48", "50", "49", "57", "52", "109", "63", "54", "65", "77", "56", "76", "69", "75", "58", "91", "149", "60", "66" ]
[ "nonn" ]
20
0
5
[ "A098550", "A251604", "A336957", "A337136", "A353239", "A359557", "A360209" ]
null
Scott R. Shannon, Jan 29 2023
2023-03-17T07:35:55
oeisdata/seq/A360/A360209.seq
759ddc45c25485b5e41647364603a19c
A360210
Indices of squares in A068869.
[ "1", "4", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "16" ]
[ "nonn", "more" ]
17
0
5
[ "A068869", "A360210" ]
null
Alexander R. Povolotsky, Jan 29 2023
2023-02-17T16:48:56
oeisdata/seq/A360/A360210.seq
2d1dc9058fb40a78316031b87f68b687
A360211
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-3*k,n-2*k).
[ "1", "2", "5", "17", "61", "221", "812", "3021", "11344", "42899", "163146", "623320", "2390653", "9198879", "35494701", "137290466", "532149805", "2066501909", "8038146035", "31312535610", "122140123201", "477002869614", "1864912495716", "7298427590543", "28588888586743", "112080607196843", "439744801379594" ]
[ "nonn" ]
14
0
5
[ "A000108", "A005317", "A024718", "A026641", "A176287", "A176332", "A360185", "A360211", "A360212" ]
null
Seiichi Manyama, Jan 30 2023
2023-03-02T09:38:37
oeisdata/seq/A360/A360211.seq
ddff2212791e7a1b04cb05f5211f766e
A360212
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-5*k,n-3*k).
[ "1", "2", "6", "19", "67", "242", "890", "3310", "12423", "46959", "178526", "681893", "2614698", "10059000", "38807021", "150080294", "581649776", "2258469988", "8783966719", "34214789901", "133450049457", "521134066663", "2037313708685", "7972641631438", "31228124666374", "122421230120657" ]
[ "nonn" ]
11
0
5
[ "A000108", "A191993", "A307354", "A360152", "A360186", "A360212" ]
null
Seiichi Manyama, Jan 30 2023
2023-03-12T11:11:39
oeisdata/seq/A360/A360212.seq
56387067a70006c82966a151f15d2191
A360213
Number of distinct stable marriage problem instances up to gender exchange.
[ "1", "10", "23436", "55037822976", "309586821132441600000", "9704204980882671472665034752000000", "3411909590124519376908837990487929799751761920000000", "24394862766922609598505096548473341484170343775734092352694570188800000000" ]
[ "nonn" ]
18
0
5
[ "A000217", "A036740", "A185141", "A343700", "A351409", "A360213" ]
null
Dan Eilers, Jan 29 2023
2023-02-18T20:50:59
oeisdata/seq/A360/A360213.seq
83fe31386f22054b3de7678cfa5a3b71
A360214
a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero octahedral numbers in exactly n ways, or -1 if no such integer exists.
[ "1", "231", "575", "721", "1618", "1750", "1877", "2240", "2736", "2995", "3105", "3080", "3500", "3311", "3920", "4151", "4280", "4495", "4719", "4621", "4675", "5041", "5164", "5291", "5060", "5591", "5480", "5566", "5635", "5755", "5985", "6216", "6080", "6279", "6320", "6510", "6655", "6636", "6870", "7145", "7195", "6999", "6971", "7296", "7211" ]
[ "nonn" ]
6
0
5
[ "A005900", "A275154", "A350205", "A360214", "A360215", "A360216" ]
null
Ilya Gutkovskiy, Jan 30 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360214.seq
c2a93967b2cbd715569ab92d3cc86880
A360215
a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero icosahedral numbers in exactly n ways, or -1 if no such integer exists.
[ "1", "1383", "4157", "6548", "8633", "9884", "12503", "12920", "15357", "15812", "18146", "18126", "19755", "20895", "22106", "23229", "23246", "23685", "22118", "25142", "25884", "27894", "29448", "28149", "29703", "30285", "31914", "30966", "34007", "34380", "34390", "35082", "35894", "34389", "36891", "37035", "37425", "35907", "35895", "38856" ]
[ "nonn" ]
5
0
5
[ "A006564", "A275154", "A350205", "A360214", "A360215", "A360216" ]
null
Ilya Gutkovskiy, Jan 30 2023
2023-01-31T08:52:05
oeisdata/seq/A360/A360215.seq
d9eddec4e2295cef7079511762968f50
A360216
a(n) is the smallest positive integer which can be represented as the sum of distinct nonzero dodecahedral numbers in exactly n ways, or -1 if no such integer exists.
[ "1", "2025", "2925", "9010", "15521", "18465", "19140", "24899", "32760", "33576", "36245", "39746", "39290", "39270", "46540", "50215", "49055", "53680", "50435", "56585", "58990", "57460", "58380", "61950", "63329", "64600", "63700", "64550", "67305", "68530", "71690" ]
[ "nonn" ]
4
0
5
[ "A006566", "A275154", "A350205", "A360214", "A360215", "A360216" ]
null
Ilya Gutkovskiy, Jan 30 2023
2023-01-31T08:52:12
oeisdata/seq/A360/A360216.seq
ff7f0b8339d882adf3a29da4252f5d0b
A360217
a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero tetrahedral numbers in exactly n ways, or -1 if no such integer exists.
[ "1", "140", "305", "315", "435", "644", "830", "1141", "1425", "1925", "2380", "3010", "3805", "4720", "5806", "7095", "8510", "10200", "12020", "14115", "16460", "19131", "21990", "25425", "29275", "33495", "37425", "42680", "48300", "54545", "60711", "68391", "75726", "84815", "93370", "103250", "114115", "125360", "137831", "150995", "165545", "179830" ]
[ "nonn" ]
8
0
5
[ "A000292", "A350205", "A350288", "A350397", "A360217", "A360218" ]
null
Ilya Gutkovskiy, Jan 30 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360217.seq
823bd30709e03d8cf24a325986e33c01
A360218
a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero square pyramidal numbers in exactly n ways, or -1 if no such integer exists.
[ "1", "5580", "2814", "1980", "1595", "1700", "2175", "2415", "2830", "3740", "4810", "5995", "7610", "9240", "11380", "13896", "16506", "19735", "23150", "27441", "32085", "36721", "42755", "49570", "56610", "65135", "73165", "83021", "93835", "105671", "118255", "132545", "147546", "163516", "182155", "201040", "222371", "244280", "267856" ]
[ "nonn" ]
14
0
5
[ "A000330", "A350206", "A350241", "A350397", "A360217", "A360218" ]
null
Ilya Gutkovskiy, Jan 30 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360218.seq
24acfe1b2cea067f31ca473ce73be833
A360219
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k) * binomial(2*(n-3*k),n-3*k).
[ "1", "2", "6", "20", "68", "240", "864", "3152", "11616", "43136", "161152", "604992", "2280416", "8624832", "32714688", "124399488", "474066560", "1810053120", "6922776576", "26517173760", "101710338048", "390603984896", "1501732753408", "5779500226560", "22263437981184", "85835254221824", "331193445626880" ]
[ "nonn" ]
42
0
5
[ "A157004", "A360219", "A360267", "A374599" ]
null
Seiichi Manyama, Jan 31 2023
2024-07-13T13:47:05
oeisdata/seq/A360/A360219.seq
87885d8e61e52cd0ee1a5be2d6da2036
A360220
Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n.
[ "1", "0", "0", "4", "5", "0", "27", "120", "333" ]
[ "nonn", "more", "hard" ]
26
0
5
[ "A287647", "A287648", "A305570", "A305571", "A349199", "A354068", "A360220" ]
null
Eduard I. Vatutin, Jan 30 2023
2023-03-24T18:21:19
oeisdata/seq/A360/A360220.seq
e984967f2deabf685d993e489180e9b8
A360221
Minimum number of intercalates in an orthogonal diagonal Latin square of order n.
[ "0", "0", "0", "12", "0", "0", "0", "2", "0" ]
[ "nonn", "more", "hard", "bref" ]
17
0
5
[ "A305570", "A305571", "A307163", "A354050", "A360221", "A360223" ]
null
Eduard I. Vatutin, Jan 30 2023
2024-10-20T13:57:38
oeisdata/seq/A360/A360221.seq
d9ceecfaa7236ecb5acd1ed38a89b82c
A360222
a(n) is the number of permutable pieces in a standard n X n X n Rubik's cube.
[ "0", "8", "20", "56", "92", "152", "212", "296", "380", "488", "596", "728", "860", "1016", "1172", "1352", "1532", "1736", "1940", "2168", "2396", "2648", "2900", "3176", "3452", "3752", "4052", "4376", "4700", "5048", "5396", "5768", "6140", "6536", "6932", "7352", "7772", "8216", "8660", "9128", "9596", "10088", "10580", "11096", "11612", "12152" ]
[ "nonn", "easy" ]
28
0
5
[ "A005897", "A010677", "A360222" ]
null
William Riley Barker, Jan 30 2023
2024-10-04T15:41:36
oeisdata/seq/A360/A360222.seq
c72840e0138d02025890ce38916a5f00
A360223
Maximum number of intercalates in an orthogonal diagonal Latin square of order n.
[ "0", "0", "0", "12", "0", "0", "18", "112", "72" ]
[ "nonn", "more", "hard" ]
17
0
5
[ "A305570", "A305571", "A307164", "A354050", "A360221", "A360223" ]
null
Eduard I. Vatutin, Jan 30 2023
2024-02-25T06:08:32
oeisdata/seq/A360/A360223.seq
b064a2bc2ad6f44328c680654abea8c8
A360224
Number of k < n such that gcd(k, n) > 1, gcd(n^2-1, k) = 1, and rad(k) does not divide n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "3", "0", "0", "0", "2", "0", "3", "0", "2", "1", "4", "0", "5", "0", "5", "2", "1", "0", "4", "0", "6", "2", "6", "0", "12", "0", "5", "3", "7", "0", "14", "0", "5", "2", "10", "0", "11", "0", "4", "5", "13", "0", "19", "0", "12", "7", "7", "1", "13", "0", "14", "3", "11", "0", "31", "0", "13", "9", "8", "2", "21", "0", "19", "7", "21", "0", "18", "2", "13", "9", "22", "0", "21", "1", "16", "10", "16" ]
[ "nonn" ]
32
0
5
[ "A045763", "A243823", "A272619", "A360224" ]
null
Michael De Vlieger, May 19 2023
2023-05-20T14:49:52
oeisdata/seq/A360/A360224.seq
51c8158b2d4b305b7b0735bd43d3f84d
A360225
a(1) = 2, a(2) = 3, a(n) = the smallest prime whose digits consist of a(n-2), followed by zero or more digits, followed by a(n).
[ "2", "3", "23", "3023", "2393023", "3023172393023", "2393023313023172393023", "3023172393023282393023313023172393023", "239302331302317239302383023172393023282393023313023172393023" ]
[ "nonn", "base" ]
9
0
5
[ "A024770", "A024785", "A048549", "A053583", "A085823", "A211682", "A250052", "A360225" ]
null
Robert C. Lyons, Jan 30 2023
2023-01-31T08:36:26
oeisdata/seq/A360/A360225.seq
3cee7fc8d334f0ff3d7ca67efbbcecc5
A360226
a(n) = sum of the first n primes whose distance to next prime is 4.
[ "7", "20", "39", "76", "119", "186", "265", "362", "465", "574", "701", "864", "1057", "1280", "1509", "1786", "2093", "2406", "2755", "3134", "3531", "3970", "4427", "4890", "5377", "5876", "6489", "7132", "7805", "8544", "9301", "10070", "10893", "11746", "12605", "13482", "14365", "15272", "16209", "17176", "18185", "19272", "20365", "21578", "22857", "24154", "25457", "26880", "28309", "29756" ]
[ "nonn", "easy" ]
82
0
5
[ "A007504", "A029710", "A086167", "A086168", "A172112", "A360226" ]
null
Artur Jasinski, Feb 01 2023
2023-02-05T07:43:50
oeisdata/seq/A360/A360226.seq
4f80e4ed29522569e73dba24a063d640
A360227
The succession of the digits of the sequence is the same when each term is multiplied by 11.
[ "1", "11", "2", "12", "21", "3", "22", "31", "33", "24", "23", "4", "13", "6", "32", "64", "25", "34", "41", "43", "66", "35", "270", "42", "7", "5", "37", "44", "51", "47", "372", "63", "8", "52", "9", "70", "46", "27", "75", "540", "74", "84", "56", "15", "17", "40", "92", "69", "38", "85", "72", "99", "770", "50", "62", "97", "82", "55", "940", "81", "49", "246", "16", "165", "18", "7440" ]
[ "base", "nonn" ]
26
0
5
[ "A360227", "A362433" ]
null
Eric Angelini, Apr 20 2023
2023-04-29T17:04:39
oeisdata/seq/A360/A360227.seq
52563791ee39c96be0ce846bc27bb107
A360228
a(n) is the least prime p such that the primes from prime(n) to p contain a complete set of residues modulo at least one of these primes.
[ "3", "7", "19", "29", "71", "103", "103", "191", "233", "317", "439", "439", "467", "467", "659", "659", "709", "1013", "1013", "1319", "1319", "1319", "1499", "1499", "1499", "1973", "1973", "2203", "2203", "2203", "3089", "3089", "3449", "3449", "3449", "3539", "3539", "3923", "3923", "4349", "4349", "4349", "4349", "4349", "4793", "4793", "4793", "4793", "5813", "5813", "5813", "5813", "5813" ]
[ "nonn" ]
20
0
5
[ "A358238", "A360228" ]
null
Robert Israel, Jan 30 2023
2025-03-25T02:30:05
oeisdata/seq/A360/A360228.seq
41ecf6524b5042fe278462532a1700bc
A360229
Row sums of triangle A360173.
[ "0", "1", "3", "6", "16", "36", "73", "156", "324", "677", "1405", "2864", "5906", "12058", "24548", "49928", "101434", "206173", "417141", "844256", "1707622", "3452998", "6970196", "14058528", "28368774", "57197983", "115239846", "232020596", "467296470", "940684267", "1892396396", "3805806218", "7654402454", "15391563411" ]
[ "nonn", "changed" ]
16
0
5
[ "A141001", "A141002", "A360173", "A360229" ]
null
John Tyler Rascoe, Jan 30 2023
2025-04-24T06:49:40
oeisdata/seq/A360/A360229.seq
9b9d6200fc522bbba81f3a0966dfa61d
A360230
a(n) = coefficient of x^n/n! in Sum_{n>=0} (1 + n*x + x^2)^n * x^n/n!.
[ "1", "1", "3", "19", "109", "921", "8911", "100003", "1307769", "18748369", "307713691", "5379610611", "106277271013", "2194176659689", "50689643777319", "1207518763542211", "31940171681228401", "862606920178886433", "25708097594461923379", "776354747057987797459", "25741373454075987900381" ]
[ "nonn" ]
10
0
5
[ "A000169", "A360230" ]
null
Paul D. Hanna, Feb 19 2023
2023-03-14T04:09:52
oeisdata/seq/A360/A360230.seq
c3f516ece61d8e147a5c7613061d165a
A360231
G.f. A(x) satisfies: [x^n] A(x)^(n+1) = [x^n] (1 + x*A(x)^(n-1))^(n+1) for n >= 0.
[ "1", "1", "1", "6", "53", "628", "9167", "156309", "3021720", "64960004", "1532234825", "39270176511", "1085601040372", "32185085432757", "1018593646880447", "34279111177431666", "1222648239226278333", "46084480032637208699", "1830881732391546532475", "76488074741796221197580", "3352854778050665597014436" ]
[ "nonn" ]
14
0
5
[ "A302702", "A302703", "A360231", "A360234", "A360235", "A360236", "A360237", "A360337", "A360345" ]
null
Paul D. Hanna, Feb 02 2023
2023-02-06T11:25:49
oeisdata/seq/A360/A360231.seq
20b4f8cbf34f92e2e76228ee7c5f47f6
A360232
G.f. Sum_{n>=0} a(n)*x^n = Sum_{n>=0} (1 + n*x + x^2)^n * x^n.
[ "1", "1", "2", "6", "16", "51", "172", "626", "2409", "9791", "41671", "185224", "855865", "4100761", "20314349", "103827684", "546388333", "2955518901", "16407286272", "93350267922", "543674327227", "3237568471183", "19693508812475", "122249256779882", "773797772369256", "4990290667614087", "32766888950422831" ]
[ "nonn" ]
13
0
5
[ "A294573", "A360232", "A360348", "A360592" ]
null
Paul D. Hanna, Feb 12 2023
2023-02-14T05:15:35
oeisdata/seq/A360/A360232.seq
21024e5672c222fff9d1e735f75058a3
A360233
a(n) = coefficient of x^n in A(x) such that x = Sum_{n=-oo..+oo} x^n * (1 - x^n/A(-x))^n.
[ "1", "1", "2", "5", "15", "49", "159", "528", "1784", "6145", "21439", "75654", "269525", "968405", "3505034", "12767879", "46773194", "172208150", "636877121", "2364867690", "8813303176", "32953850231", "123589941046", "464792925189", "1752421377254", "6622694660061", "25082577300996", "95188198019919", "361915271697707" ]
[ "nonn" ]
7
0
5
[ "A355869", "A360233" ]
null
Paul D. Hanna, Feb 13 2023
2023-02-13T11:42:22
oeisdata/seq/A360/A360233.seq
e654319ee6d7e0ac4ec2b42f7d4f4b50
A360234
G.f. A(x) satisfies: [x^n] A(x)^(n+1) = [x^n] (1 + x*A(x)^(n+2))^(n+1) for n >= 0.
[ "1", "1", "4", "33", "414", "6750", "131963", "2957899", "73968136", "2027178710", "60143834893", "1914750144642", "64984397381766", "2339387034919340", "88976089246855623", "3563952072597604091", "149941204887915187568", "6610797722288579969347", "304837386103152855175255", "14675559490665539299350303" ]
[ "nonn" ]
19
0
5
[ "A302702", "A302703", "A360231", "A360234", "A360235", "A360236", "A360237", "A360338", "A360346" ]
null
Paul D. Hanna, Jan 30 2023
2023-02-06T11:28:07
oeisdata/seq/A360/A360234.seq
25fbf32c0b70b89b30c485d4ccadc67a
A360235
G.f. A(x) satisfies: [x^n] A(x)^(n+1) = [x^n] (1 + x*A(x)^(n+3))^(n+1) for n >= 0.
[ "1", "1", "5", "48", "673", "12057", "256763", "6232909", "168035350", "4945380012", "157008686993", "5331606427775", "192417007138176", "7344652874314128", "295384546093569838", "12478509340848604628", "552330553975194126634", "25560514938260757190962", "1234444956694450007259989", "62114842767595821207341042" ]
[ "nonn" ]
21
0
5
[ "A302702", "A302703", "A360231", "A360234", "A360235", "A360236", "A360237", "A360338", "A360347" ]
null
Paul D. Hanna, Jan 30 2023
2023-02-06T11:28:54
oeisdata/seq/A360/A360235.seq
be0636eb9c1c297db713187339e747ad
A360236
G.f. A(x) satisfies: [x^n] A(x)^(n+1) = [x^n] (1 + x*A(x)^(n+4))^(n+1) for n >= 0.
[ "1", "1", "6", "66", "1028", "20138", "464863", "12162876", "351915528", "11075859686", "374858234365", "13530279602015", "517628371405448", "20890826296067329", "886175281852068632", "39393952245422498344", "1830781283537184304756", "88768944166701791039297", "4482797026386165709436753", "235417696462456105986818505" ]
[ "nonn" ]
19
0
5
[ "A302702", "A302703", "A360231", "A360234", "A360235", "A360236", "A360237" ]
null
Paul D. Hanna, Jan 30 2023
2023-02-02T21:10:38
oeisdata/seq/A360/A360236.seq
a0252b96c01240a12c27596bda34ae66
A360237
G.f. A(x) satisfies: [x^n] A(x)^(n+1) = [x^n] (1 + x*A(x)^(n+5))^(n+1) for n >= 0.
[ "1", "1", "7", "87", "1495", "31865", "793769", "22290228", "689397657", "23116772771", "831159921411", "31787496335409", "1285410740283302", "54708408148614317", "2441969507507612684", "113988651908380638224", "5551479742274622439616", "281540748098045175486249", "14843765603832700589293465" ]
[ "nonn" ]
23
0
5
[ "A302702", "A302703", "A360231", "A360234", "A360235", "A360236", "A360237" ]
null
Paul D. Hanna, Jan 30 2023
2023-02-05T03:20:14
oeisdata/seq/A360/A360237.seq
93ed4ac74e6f08abaa0eaf1de97984fb
A360238
a(n) = [y^n*x^n/n] log( Sum_{m>=0} (m + y)^(2*m) * x^m ) for n >= 1.
[ "2", "42", "1376", "60934", "3377252", "224036904", "17282039280", "1519096411230", "149867251224092", "16398595767212452", "1971137737765484444", "258215735255164847944", "36617351885600586385222", "5588967440618883091216208", "913592455995572681826313856", "159241707066923571547572653630" ]
[ "nonn" ]
20
0
5
[ "A000984", "A059304", "A098658", "A266526", "A360238", "A360239", "A360348" ]
null
Paul D. Hanna, Feb 11 2023
2023-02-13T03:42:24
oeisdata/seq/A360/A360238.seq
54f8d6d813e30950049aa8bbd51c45e9
A360239
G.f. A(x) = exp( Sum_{k>=1} A360238(k) * x^k/k ), where A360238(k) = [y^k*x^k/k] log( Sum_{m>=0} (m + y)^(2*m) * x^m ) for k >= 1.
[ "1", "2", "23", "502", "16414", "716936", "39167817", "2567058766", "196159319943", "17118727499178", "1679643875717867", "183020512751712554", "21928106267349661127", "2865208654370111795940", "405479888251812823615679", "61785441098476295018209264", "10085622916281496742096639996" ]
[ "nonn" ]
10
0
5
[ "A000108", "A000984", "A360238", "A360239", "A360349" ]
null
Paul D. Hanna, Feb 11 2023
2023-02-13T03:41:48
oeisdata/seq/A360/A360239.seq
926c1ed0221f9a73ed7d9dedb473db34
A360240
Weakly decreasing triples of positive integers sorted lexicographically and concatenated.
[ "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "2", "3", "1", "1", "3", "2", "1", "3", "2", "2", "3", "3", "1", "3", "3", "2", "3", "3", "3", "4", "1", "1", "4", "2", "1", "4", "2", "2", "4", "3", "1", "4", "3", "2", "4", "3", "3", "4", "4", "1", "4", "4", "2", "4", "4", "3", "4", "4", "4", "5", "1", "1", "5", "2", "1", "5", "2", "2", "5", "3", "1", "5", "3", "2", "5", "3", "3", "5", "4", "1", "5", "4", "2", "5", "4", "3" ]
[ "nonn" ]
7
0
5
[ "A002024", "A003056", "A056556", "A056557", "A056558", "A069905", "A070770", "A158842", "A194848", "A330709", "A331195", "A333516", "A360010", "A360240" ]
null
Gus Wiseman, Feb 11 2023
2023-02-11T20:32:28
oeisdata/seq/A360/A360240.seq
2cd86213e1411d819c01f7dbcbd62f16
A360241
Number of integer partitions of n whose distinct parts have integer mean.
[ "0", "1", "2", "2", "4", "3", "8", "6", "13", "13", "22", "19", "43", "34", "56", "66", "97", "92", "156", "143", "233", "256", "322", "341", "555", "542", "710", "831", "1098", "1131", "1644", "1660", "2275", "2484", "3035", "3492", "4731", "4848", "6063", "6893", "8943", "9378", "12222", "13025", "16520", "18748", "22048", "24405", "31446", "33698", "41558" ]
[ "nonn" ]
8
0
5
[ "A000009", "A000041", "A000975", "A008284", "A051293", "A058398", "A067340", "A067538", "A067539", "A078174", "A082550", "A102627", "A116608", "A240219", "A316313", "A316413", "A325347", "A326567", "A326568", "A326619", "A326620", "A326621", "A326622", "A326669", "A327475", "A327482", "A328966", "A349156", "A360069", "A360071", "A360241", "A360242", "A360243", "A360246", "A360247", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 02 2023
2023-02-05T23:07:05
oeisdata/seq/A360/A360241.seq
02b130272b72887bad04350b9087a7fa
A360242
Number of integer partitions of n where the parts do not have the same mean as the distinct parts.
[ "0", "0", "0", "0", "1", "3", "3", "9", "11", "19", "25", "43", "49", "82", "103", "136", "183", "258", "314", "435", "524", "687", "892", "1150", "1378", "1788", "2241", "2773", "3399", "4308", "5142", "6501", "7834", "9600", "11726", "14099", "16949", "20876", "25042", "30032", "35732", "43322", "51037", "61650", "72807", "86319", "102983", "122163" ]
[ "nonn" ]
9
0
5
[ "A000009", "A000041", "A008284", "A051293", "A058398", "A067340", "A067538", "A102627", "A116608", "A240219", "A316313", "A316413", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A349156", "A360068", "A360071", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 04 2023
2023-02-06T10:06:20
oeisdata/seq/A360/A360242.seq
31a45098c58017bfa452682b2920e2e3
A360243
Number of integer partitions of n where the parts have the same mean as the distinct parts.
[ "1", "1", "2", "3", "4", "4", "8", "6", "11", "11", "17", "13", "28", "19", "32", "40", "48", "39", "71", "55", "103", "105", "110", "105", "197", "170", "195", "237", "319", "257", "462", "341", "515", "543", "584", "784", "1028", "761", "973", "1153", "1606", "1261", "2137", "1611", "2368", "2815", "2575", "2591", "4393", "3798", "4602", "4663", "5777", "5121" ]
[ "nonn" ]
5
0
5
[ "A000009", "A000041", "A008284", "A051293", "A058398", "A067340", "A067538", "A102627", "A116608", "A240219", "A316313", "A316413", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A349156", "A360068", "A360069", "A360071", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 04 2023
2023-02-06T10:06:16
oeisdata/seq/A360/A360243.seq
5b93db83556c6a1cc6770786cdebc43b
A360244
Number of integer partitions of n where the parts do not have the same median as the distinct parts.
[ "0", "0", "0", "0", "1", "3", "3", "9", "11", "17", "23", "37", "42", "68", "87", "110", "153", "209", "261", "352", "444", "573", "750", "949", "1187", "1508", "1909", "2367", "2938", "3662", "4507", "5576", "6826", "8359", "10203", "12372", "15011", "18230", "21996", "26518", "31779", "38219", "45682", "54660", "65112", "77500", "92089", "109285" ]
[ "nonn" ]
7
0
5
[ "A000009", "A000041", "A000975", "A008284", "A027193", "A067659", "A116608", "A240219", "A325347", "A326619", "A326620", "A326621", "A359889", "A359890", "A359893", "A359894", "A359901", "A359902", "A359907", "A359908", "A360068", "A360071", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360248", "A360249", "A360250", "A360251" ]
null
Gus Wiseman, Feb 05 2023
2023-02-06T10:06:12
oeisdata/seq/A360/A360244.seq
2456e6043fe94c1034ea083adb27bb53
A360245
Number of integer partitions of n where the parts have the same median as the distinct parts.
[ "1", "1", "2", "3", "4", "4", "8", "6", "11", "13", "19", "19", "35", "33", "48", "66", "78", "88", "124", "138", "183", "219", "252", "306", "388", "450", "527", "643", "780", "903", "1097", "1266", "1523", "1784", "2107", "2511", "2966", "3407", "4019", "4667", "5559", "6364", "7492", "8601", "10063", "11634", "13469", "15469", "17985", "20558", "23812" ]
[ "nonn" ]
5
0
5
[ "A000009", "A000041", "A000975", "A008284", "A027193", "A067659", "A116608", "A240219", "A325347", "A326619", "A326620", "A326621", "A359889", "A359890", "A359893", "A359894", "A359901", "A359902", "A359907", "A359908", "A360071", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360248", "A360249", "A360250", "A360251" ]
null
Gus Wiseman, Feb 05 2023
2023-02-06T10:06:07
oeisdata/seq/A360/A360245.seq
74c03ab6f3a4ab6be21426a20217db6f
A360246
Numbers for which the prime indices do not have the same mean as the distinct prime indices.
[ "12", "18", "20", "24", "28", "40", "44", "45", "48", "50", "52", "54", "56", "60", "63", "68", "72", "75", "76", "80", "84", "88", "92", "96", "98", "99", "104", "108", "112", "116", "117", "120", "124", "126", "132", "135", "136", "140", "144", "147", "148", "150", "152", "153", "156", "160", "162", "164", "168", "171", "172", "175", "176", "180", "184", "188", "189" ]
[ "nonn" ]
8
0
5
[ "A000975", "A001222", "A051293", "A056239", "A058398", "A067340", "A067538", "A088529", "A088530", "A112798", "A114638", "A124010", "A316413", "A324570", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A359903", "A360005", "A360068", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360248", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 07 2023
2023-02-08T13:12:01
oeisdata/seq/A360/A360246.seq
171584c02f78f356ec085c50588c4a07
A360247
Numbers for which the prime indices have the same mean as the distinct prime indices.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "19", "21", "22", "23", "25", "26", "27", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "46", "47", "49", "51", "53", "55", "57", "58", "59", "61", "62", "64", "65", "66", "67", "69", "70", "71", "73", "74", "77", "78", "79", "81", "82", "83", "85", "86", "87", "89", "90", "91", "93", "94", "95", "97", "100", "101", "102", "103", "105", "106", "107", "109", "110", "111", "113", "114", "115", "118", "119", "121", "122", "123", "125", "127", "128", "129", "130" ]
[ "nonn" ]
7
0
5
[ "A000975", "A001222", "A008284", "A051293", "A056239", "A058398", "A067340", "A067538", "A088529", "A088530", "A112798", "A114638", "A116608", "A124010", "A316413", "A324570", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A359903", "A360005", "A360068", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360248", "A360249", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 07 2023
2023-05-22T05:43:18
oeisdata/seq/A360/A360247.seq
89885b856cce1cfda1a2684149a91348
A360248
Numbers for which the prime indices do not have the same median as the distinct prime indices.
[ "12", "18", "20", "24", "28", "40", "44", "45", "48", "50", "52", "54", "56", "60", "63", "68", "72", "75", "76", "80", "84", "88", "92", "96", "98", "99", "104", "108", "112", "116", "117", "120", "124", "132", "135", "136", "140", "144", "147", "148", "150", "152", "153", "156", "160", "162", "164", "168", "171", "172", "175", "176", "184", "188", "189", "192", "200" ]
[ "nonn" ]
7
0
5
[ "A000975", "A001222", "A056239", "A078174", "A112798", "A316413", "A324570", "A325347", "A326567", "A326568", "A326619", "A326620", "A359890", "A359893", "A359901", "A359907", "A359908", "A360005", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360248", "A360249", "A360453", "A360454", "A360455", "A360456" ]
null
Gus Wiseman, Feb 07 2023
2023-02-09T20:49:19
oeisdata/seq/A360/A360248.seq
a173293e6f58841fd457a9b7f437688c
A360249
Numbers for which the prime indices have the same median as the distinct prime indices.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "19", "21", "22", "23", "25", "26", "27", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "46", "47", "49", "51", "53", "55", "57", "58", "59", "61", "62", "64", "65", "66", "67", "69", "70", "71", "73", "74", "77", "78", "79", "81", "82", "83", "85", "86", "87", "89", "90", "91", "93", "94", "95", "97", "100", "101", "102", "103", "105", "106", "107", "109", "110", "111", "113", "114", "115", "118", "119", "121", "122", "123", "125", "126", "127", "128", "129", "130" ]
[ "nonn" ]
8
0
5
[ "A000975", "A001222", "A056239", "A078174", "A112798", "A240219", "A316413", "A324570", "A325347", "A326567", "A326568", "A326619", "A326620", "A359889", "A359890", "A359893", "A359894", "A359901", "A359903", "A359907", "A359908", "A360005", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360248", "A360249", "A360252", "A360253", "A360453", "A360454", "A360455", "A360456" ]
null
Gus Wiseman, Feb 07 2023
2023-05-22T05:58:10
oeisdata/seq/A360/A360249.seq
4a696cd065b9635100c8e8343937c1bd
A360250
Number of integer partitions of n where the parts have greater mean than the distinct parts.
[ "0", "0", "0", "0", "0", "1", "0", "2", "2", "3", "3", "9", "5", "13", "15", "18", "20", "37", "34", "59", "51", "68", "92", "134", "121", "167", "203", "251", "282", "387", "375", "537", "561", "714", "888", "958", "1042", "1408", "1618", "1939", "2076", "2650", "2764", "3479", "3863", "4431", "5387", "6520", "6688", "8098", "9041", "10614", "12084", "14773", "15469" ]
[ "nonn" ]
5
0
5
[ "A000009", "A000041", "A000975", "A008284", "A058398", "A067538", "A102627", "A116608", "A240219", "A316313", "A316413", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A359889", "A359890", "A359894", "A360068", "A360071", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 06 2023
2023-02-07T12:44:28
oeisdata/seq/A360/A360250.seq
c9eebe135a84fe8473d6d0fc1e67fa11
A360251
Number of integer partitions of n where the parts have lesser mean than the distinct parts.
[ "0", "0", "0", "0", "1", "2", "3", "7", "9", "16", "22", "34", "44", "69", "88", "118", "163", "221", "280", "376", "473", "619", "800", "1016", "1257", "1621", "2038", "2522", "3117", "3921", "4767", "5964", "7273", "8886", "10838", "13141", "15907", "19468", "23424", "28093", "33656", "40672", "48273", "58171", "68944", "81888", "97596", "115643" ]
[ "nonn" ]
6
0
5
[ "A000009", "A000041", "A000975", "A008284", "A058398", "A067538", "A102627", "A116608", "A240219", "A316313", "A316413", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A359889", "A359890", "A359894", "A360068", "A360071", "A360241", "A360242", "A360243", "A360244", "A360245", "A360246", "A360247", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 06 2023
2023-02-07T12:43:57
oeisdata/seq/A360/A360251.seq
e139a0bea80cfe3a7fd4270e47887f6c
A360252
Numbers for which the prime indices have greater mean than the distinct prime indices.
[ "18", "50", "54", "75", "98", "108", "147", "150", "162", "242", "245", "250", "294", "324", "338", "350", "363", "375", "450", "486", "490", "500", "507", "578", "588", "605", "648", "686", "722", "726", "735", "750", "845", "847", "867", "882", "972", "1014", "1029", "1050", "1058", "1078", "1083", "1125", "1183", "1210", "1250", "1274", "1350", "1372" ]
[ "nonn" ]
5
0
5
[ "A000975", "A001222", "A051293", "A056239", "A058398", "A067340", "A067538", "A112798", "A316413", "A324570", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A359903", "A360005", "A360241", "A360242", "A360243", "A360246", "A360247", "A360248", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 09 2023
2023-02-10T14:29:35
oeisdata/seq/A360/A360252.seq
8809af1f5b354cb02013626b00acf0da
A360253
Numbers for which the prime indices have lesser mean than the distinct prime indices.
[ "12", "20", "24", "28", "40", "44", "45", "48", "52", "56", "60", "63", "68", "72", "76", "80", "84", "88", "92", "96", "99", "104", "112", "116", "117", "120", "124", "126", "132", "135", "136", "140", "144", "148", "152", "153", "156", "160", "164", "168", "171", "172", "175", "176", "180", "184", "188", "189", "192", "198", "200", "204", "207", "208", "212", "220" ]
[ "nonn" ]
7
0
5
[ "A000975", "A001222", "A051293", "A056239", "A058398", "A067340", "A067538", "A112798", "A316413", "A324570", "A326567", "A326568", "A326619", "A326620", "A326621", "A327482", "A359903", "A360005", "A360241", "A360242", "A360243", "A360246", "A360247", "A360248", "A360250", "A360251", "A360252", "A360253" ]
null
Gus Wiseman, Feb 09 2023
2023-02-10T14:29:29
oeisdata/seq/A360/A360253.seq
eff9f90a62e260f0ac2fe44a22c8365d
A360254
Number of integer partitions of n with more adjacent equal parts than distinct parts.
[ "0", "0", "0", "1", "1", "1", "3", "4", "7", "10", "12", "18", "28", "36", "52", "68", "92", "119", "161", "204", "269", "355", "452", "571", "738", "921", "1167", "1457", "1829", "2270", "2834", "3483", "4314", "5300", "6502", "7932", "9665", "11735", "14263", "17227", "20807", "25042", "30137", "36099", "43264", "51646", "61608", "73291", "87146", "103296" ]
[ "nonn" ]
9
0
5
[ "A000009", "A000041", "A000975", "A008284", "A027193", "A067538", "A102627", "A116608", "A237363", "A240219", "A325347", "A359893", "A359894", "A359901", "A359902", "A359907", "A359908", "A360071", "A360244", "A360254", "A360555", "A360556", "A360558", "A360688" ]
null
Gus Wiseman, Feb 20 2023
2023-02-21T07:34:04
oeisdata/seq/A360/A360254.seq
74b21a11925a9aeebbe24c82285d88b9
A360255
Irregular triangle (an infinite binary tree) read by rows: see Comments section for definition.
[ "0", "1", "3", "6", "2", "10", "7", "5", "15", "13", "11", "9", "21", "20", "4", "18", "2", "16", "14", "28", "12", "28", "12", "26", "8", "24", "22", "20", "36", "21", "19", "37", "21", "17", "35", "17", "33", "13", "31", "11", "29", "27", "45", "11", "31", "9", "29", "27", "47", "31", "7", "27", "25", "45", "7", "27", "23", "43", "23", "41", "19", "39", "17", "37", "35", "55", "22", "42", "18" ]
[ "nonn", "tabf" ]
14
0
5
[ "A000217", "A141001", "A141002", "A321535", "A360173", "A360255" ]
null
John Tyler Rascoe, Jan 30 2023
2023-02-13T08:57:34
oeisdata/seq/A360/A360255.seq
00b0f6f8a552e43f6a9f9930f8152d30
A360256
Number of ways to tile an n X n square using rectangles with distinct height X width dimensions.
[ "1", "1", "33", "513", "14409", "693025", "50447161" ]
[ "nonn", "more" ]
51
0
5
[ "A004003", "A065072", "A099390", "A182275", "A360256", "A360498", "A360499", "A360725" ]
null
Scott R. Shannon, Feb 17 2023
2023-02-24T07:02:05
oeisdata/seq/A360/A360256.seq
410179542fb0066c7e83d1d498428881
A360257
a(1) = 1; for n > 1, a(n) is the number of preceding terms having the same sum of divisors as a(n-1).
[ "1", "1", "2", "1", "3", "1", "4", "1", "5", "1", "6", "1", "7", "1", "8", "1", "9", "1", "10", "1", "11", "2", "2", "3", "2", "4", "2", "5", "2", "6", "3", "3", "4", "3", "5", "3", "6", "4", "4", "5", "4", "6", "5", "5", "6", "6", "7", "2", "7", "3", "7", "4", "7", "5", "7", "6", "8", "2", "8", "3", "8", "4", "8", "5", "8", "6", "9", "2", "9", "3", "9", "4", "9", "5", "9", "6", "10", "2", "10", "3", "10", "4", "10", "5", "10", "6", "11", "12", "1", "12", "2", "11", "13", "1" ]
[ "nonn" ]
13
0
5
[ "A000203", "A276457", "A356348", "A360257" ]
null
Scott R. Shannon, Jan 31 2023
2023-01-31T08:21:49
oeisdata/seq/A360/A360257.seq
9703ee0faef4ffebce2167ea786cfe04
A360258
a(n) is the smallest k such that A360097(k) = n.
[ "13", "14", "20", "7", "5", "10", "4", "9", "63", "6", "42", "1590", "1", "2", "5172911835", "974749335", "21", "26135070" ]
[ "nonn", "more" ]
33
0
5
[ "A018252", "A124522", "A360097", "A360258" ]
null
Jean-Marc Rebert, Feb 01 2023
2023-02-17T20:30:31
oeisdata/seq/A360/A360258.seq
c68cb24afbbff9dd3c6df8b9049b01d8
A360259
a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that F(2) + ... + F(1+k) >= n (where F(m) denotes A000045(m), the m-th Fibonacci number); a(n) = k + a(F(2) + ... + F(1+k) - n).
[ "0", "1", "3", "2", "6", "4", "3", "10", "6", "7", "5", "4", "15", "8", "9", "11", "7", "8", "6", "5", "21", "10", "11", "13", "12", "16", "9", "10", "12", "8", "9", "7", "6", "28", "12", "13", "15", "14", "18", "16", "15", "22", "11", "12", "14", "13", "17", "10", "11", "13", "9", "10", "8", "7", "36", "14", "15", "17", "16", "20", "18", "17", "24", "20", "21", "19", "18", "29", "13", "14", "16" ]
[ "nonn", "look" ]
13
0
5
[ "A000045", "A001911", "A095791", "A227192", "A360259", "A360260", "A360265" ]
null
Rémy Sigrist, Jan 31 2023
2023-02-02T14:44:23
oeisdata/seq/A360/A360259.seq
c198e21faef37f5359cb18f47a22b804
A360260
a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that T(3) + ... + T(2+k) >= n (where T(m) denotes A000073(m), the m-th tribonacci number); a(n) = k + a(T(3) + ... + T(2+k) - n).
[ "0", "1", "3", "2", "5", "6", "4", "3", "8", "10", "9", "6", "7", "5", "4", "12", "11", "14", "15", "13", "8", "9", "11", "10", "7", "8", "6", "5", "16", "17", "15", "14", "19", "21", "20", "17", "18", "10", "11", "13", "12", "15", "16", "14", "9", "10", "12", "11", "8", "9", "7", "6", "21", "23", "22", "19", "20", "18", "17", "25", "24", "27", "28", "26", "21", "22", "24", "23", "12", "13", "15" ]
[ "nonn", "look" ]
10
0
5
[ "A000073", "A027084", "A356895", "A360259", "A360260" ]
null
Rémy Sigrist, Jan 31 2023
2023-02-02T14:43:53
oeisdata/seq/A360/A360260.seq
9d1c177a078bbe75c347fc52247bfbea
A360261
Determinant of the pentadiagonal symmetric n X n Toeplitz Matrix with a=b=1, c=2.
[ "1", "1", "0", "-1", "7", "32", "9", "1", "-32", "495", "567", "288", "-935", "3025", "15840", "9503", "2023", "-29920", "236457", "312481", "304096", "-639153", "1252503", "7566624", "7396345", "2283121", "-20452896", "108556415", "167727175", "236683040", "-376631991", "491819329", "3473805280", "5032011951", "2018956023", "-12052223712", "47535816601" ]
[ "sign", "easy" ]
9
0
5
[ "A071534", "A360261" ]
null
R. J. Mathar, Jan 31 2023
2023-06-24T16:02:58
oeisdata/seq/A360/A360261.seq
40d01ad749e9ad8e06e66b76e5375962
A360262
Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=b=1, c=3.
[ "1", "1", "0", "-4", "56", "177", "25", "-248", "1536", "19448", "10025", "2313", "-78584", "1525084", "2046000", "1990649", "-12721279", "80406480", "282880000", "276053680", "-672007599", "1449521681", "28914914000", "32747999676", "14429332456", "-221875825343" ]
[ "sign", "easy" ]
6
0
5
null
null
R. J. Mathar, Jan 31 2023
2024-06-10T00:17:16
oeisdata/seq/A360/A360262.seq
07aaa4a18d6502f7afc8bae69ea723a9
A360263
Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=3, b=c=1.
[ "1", "3", "8", "20", "48", "115", "273", "648", "1536", "3640", "8625", "20435", "48416", "114708", "271768", "643875", "1525473", "3614160", "8562688", "20286768", "48063521", "113872355", "269787000", "639180820", "1514350656", "3587807763" ]
[ "nonn", "easy" ]
4
0
5
null
null
R. J. Mathar, Jan 31 2023
2023-01-31T06:50:57
oeisdata/seq/A360/A360263.seq
59d63fa655d6fd6b00ccedd1fe894662
A360264
Sum of mass(k/n) for all k, 1 <= k <= n, that are relatively prime to n.
[ "1", "2", "6", "8", "18", "12", "34", "26", "42", "32", "74", "36", "98", "56", "80", "78", "150", "64", "178", "92", "140", "116", "238", "100", "238", "148", "222", "160", "338", "112", "374", "214", "280", "220", "348", "180", "486", "260", "356", "248", "562", "192", "602", "316", "388", "344", "682", "264", "662", "328", "528", "404", "810", "308", "688", "424" ]
[ "nonn" ]
26
0
5
[ "A000010", "A049835", "A360264" ]
null
Jeffrey Shallit, Jan 31 2023
2024-12-13T10:25:21
oeisdata/seq/A360/A360264.seq
ff68516883a0dc72a3a22c9ff1c8bd3b
A360265
a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that t(k) >= n (where t(m) denotes A000217(m), the m-th triangular number); a(n) = k + a(t(k) - n).
[ "0", "1", "3", "2", "6", "4", "3", "6", "7", "5", "4", "11", "7", "8", "6", "5", "10", "12", "8", "9", "7", "6", "10", "11", "13", "9", "10", "8", "7", "14", "11", "12", "14", "10", "11", "9", "8", "16", "15", "12", "13", "15", "11", "12", "10", "9", "15", "17", "16", "13", "14", "16", "12", "13", "11", "10", "15", "16", "18", "17", "14", "15", "17", "13", "14", "12", "11", "23", "16", "17", "19" ]
[ "nonn", "look" ]
9
0
5
[ "A000217", "A002024", "A360259", "A360265" ]
null
Rémy Sigrist, Jan 31 2023
2023-02-02T14:43:17
oeisdata/seq/A360/A360265.seq
336ffe30096ac5e3796dd07411e52f33
A360266
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(2*(n-2*k),n-2*k).
[ "1", "2", "6", "22", "82", "312", "1210", "4752", "18834", "75184", "301856", "1217604", "4930626", "20032052", "81615072", "333328532", "1364264250", "5594210292", "22977466864", "94517423444", "389316529512", "1605533230256", "6628467569292", "27393187077144", "113310732332274", "469101108803052" ]
[ "nonn" ]
19
0
5
[ "A006139", "A157004", "A360266", "A360267", "A374598" ]
null
Seiichi Manyama, Jan 31 2023
2024-07-13T13:47:14
oeisdata/seq/A360/A360266.seq
a391400bdd366dc735593df3dcbd1339
A360267
a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*(n-3*k),n-3*k).
[ "1", "2", "6", "20", "72", "264", "984", "3712", "14136", "54224", "209200", "810912", "3155616", "12320512", "48239232", "189336192", "744722400", "2934759360", "11584470336", "45796087680", "181285742592", "718498695424", "2850802065152", "11322567705600", "45011437903104", "179088911779328" ]
[ "nonn" ]
23
0
5
[ "A006139", "A360219", "A360266", "A360267", "A374599" ]
null
Seiichi Manyama, Jan 31 2023
2024-07-13T13:47:10
oeisdata/seq/A360/A360267.seq
e100b08d790d96e8515490904e670b0c
A360268
A version of the Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,...,n in a circle, increasing clockwise. Starting with i=1, delete the integer 5 places clockwise from i. Repeat, counting 5 places from the next undeleted integer, until only one integer remains.
[ "1", "1", "1", "3", "4", "4", "3", "1", "7", "3", "9", "3", "9", "1", "7", "13", "2", "8", "14", "20", "5", "11", "17", "23", "4", "10", "16", "22", "28", "4", "10", "16", "22", "28", "34", "4", "10", "16", "22", "28", "34", "40", "3", "9", "15", "21", "27", "33", "39", "45", "51", "5", "11", "17", "23", "29", "35", "41", "47", "53", "59", "3", "9", "15", "21", "27", "33", "39", "45", "51", "57", "63", "69", "1", "7", "13", "19", "25" ]
[ "nonn" ]
51
0
5
[ "A006257", "A054995", "A088333", "A181281", "A198789", "A360268" ]
null
Benjamin Lilley, Jan 31 2023
2023-03-17T07:23:32
oeisdata/seq/A360/A360268.seq
98849003e363b4632467ae3dd9609286
A360269
Least sum of 2's and 3's required to build n using +, * and parentheses.
[ "2", "3", "4", "5", "5", "7", "6", "6", "7", "8", "7", "10", "9", "8", "8", "10", "8", "11", "9", "10", "10", "12", "9", "10", "11", "9", "11", "11", "10", "13", "10", "11", "12", "12", "10", "14", "12", "13", "11", "15", "12", "14", "12", "11", "14", "13", "11", "14", "12", "13", "13", "15", "11", "13", "13", "14", "13", "16", "12", "16", "14", "13", "12", "15", "13", "15", "14", "15", "14" ]
[ "nonn" ]
20
0
5
[ "A000040", "A025280", "A360269" ]
null
Tamas Sandor Nagy, Jan 31 2023
2023-02-23T13:21:35
oeisdata/seq/A360/A360269.seq
4668b405ae3668deef82643091f3c2b3
A360270
Decimal expansion of the kelvin-kilogram relationship (k/c^2) according to the 2019 SI system in units kg.
[ "1", "5", "3", "6", "1", "7", "9", "1", "8", "7", "2", "4", "0", "3", "7", "2", "2", "3", "4", "7", "6", "2", "7", "2", "5", "1", "3", "5", "8", "7", "7", "4", "4", "0", "1", "4", "6", "9", "0", "2", "9", "4", "8", "0", "4", "8", "1", "2", "5", "4", "2", "2", "3", "2", "7", "3", "4", "4", "4", "3", "2", "7", "2", "0", "2", "1", "1", "5", "6", "3", "1", "2", "7", "0", "9", "9", "9", "3", "1", "7", "1", "9", "0", "9", "0", "7" ]
[ "cons", "easy", "nonn" ]
12
0
5
[ "A003678", "A070063", "A360270" ]
null
Marco Ripà, Jan 31 2023
2025-02-13T04:03:40
oeisdata/seq/A360/A360270.seq
e5493e2cacc48fb09708a8d7216d898f
A360271
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k) * Catalan(n-3*k).
[ "1", "1", "2", "5", "13", "38", "117", "373", "1222", "4085", "13877", "47766", "166229", "583893", "2067414", "7371093", "26440789", "95355990", "345538389", "1257486165", "4593933398", "16841578325", "61938532181", "228454719830", "844882459989", "3132258655573", "11638656376150", "43337083401557" ]
[ "nonn" ]
15
0
5
[ "A000108", "A157003", "A360219", "A360271", "A360272" ]
null
Seiichi Manyama, Jan 31 2023
2024-09-29T13:17:25
oeisdata/seq/A360/A360271.seq
efab29806f231c6ec5953021ab1a6d72
A360272
a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * Catalan(n-3*k).
[ "1", "1", "2", "5", "15", "46", "147", "485", "1642", "5669", "19883", "70646", "253755", "919925", "3361546", "12368661", "45786219", "170400470", "637200555", "2392962645", "9021255722", "34128098389", "129519490219", "492966689110", "1881289209003", "7197100511317", "27595769836714", "106032318322517" ]
[ "nonn" ]
16
0
5
[ "A000108", "A052709", "A125305", "A360267", "A360271", "A360272", "A360274" ]
null
Seiichi Manyama, Jan 31 2023
2024-09-29T13:17:20
oeisdata/seq/A360/A360272.seq
a14a0a4b564d0f70f50864e3dcef483e
A360273
a(n) = Sum_{k=0..floor(n/2)} Catalan(n-2*k).
[ "1", "1", "3", "6", "17", "48", "149", "477", "1579", "5339", "18375", "64125", "226387", "807025", "2900827", "10501870", "38258497", "140146660", "515897197", "1907409850", "7080017617", "26373676870", "98562581257", "369433290520", "1388466728581", "5231379691972" ]
[ "nonn", "easy" ]
16
0
5
[ "A000108", "A014137", "A360273", "A360274" ]
null
Seiichi Manyama, Jan 31 2023
2024-09-08T15:49:31
oeisdata/seq/A360/A360273.seq
7721b288b6658b22440184bbdd5f10c0
A360274
a(n) = Sum_{k=0..floor(n/3)} Catalan(n-3*k).
[ "1", "1", "2", "6", "15", "44", "138", "444", "1474", "5000", "17240", "60260", "213012", "760140", "2734700", "9907857", "36117810", "132379490", "487546557", "1803381000", "6696499910", "24953813577", "93285944640", "349756113560", "1314857960901", "4955232346092", "18717109185712", "70848408876905" ]
[ "nonn", "easy" ]
13
0
5
[ "A000108", "A014137", "A360273", "A360274" ]
null
Seiichi Manyama, Jan 31 2023
2023-03-12T11:04:07
oeisdata/seq/A360/A360274.seq
65d08a08a6aa8140b913ab68193f6c3e
A360275
Number of unordered quadruples of self-avoiding paths with nodes that cover all vertices of a convex n-gon.
[ "0", "0", "0", "0", "0", "105", "3780", "81900", "1386000", "20207880", "266666400", "3277354080", "38198160000", "427365818880", "4629059635200", "48842864179200", "504335346278400", "5114054709319680", "51064119467827200", "503151159589478400", "4900668252598272000", "47248486914198011904", "451429610841538560000" ]
[ "nonn" ]
9
0
5
[ "A001792", "A332426", "A359404", "A360275" ]
null
Ivaylo Kortezov, Feb 01 2023
2023-02-17T20:22:25
oeisdata/seq/A360/A360275.seq
188f7d80785ec5101022b8da3911787f
A360276
Number of unordered quadruples of self-avoiding paths with nodes that cover all vertices of a convex n-gon; one-node paths are allowed.
[ "0", "0", "10", "105", "1015", "9625", "90972", "861420", "8191920", "78309000", "752317280", "7257522272", "70223986560", "680703296000", "6601793730560", "63984047339520", "619018056228864", "5972223901440000", "57415027394027520", "549677356175073280", "5238367168966328320", "49678823782558924800", "468783944069762252800" ]
[ "nonn" ]
9
0
5
[ "A001792", "A359405", "A360021", "A360276" ]
null
Ivaylo Kortezov, Feb 01 2023
2023-02-17T20:14:09
oeisdata/seq/A360/A360276.seq
0f62edc9e9a774d997807cd22ee49929
A360277
Primes p that are congruent to 1 mod 2*k, where k = primepi(p) is the index of the prime.
[ "11", "13", "1087", "64591", "64601", "64661", "3523969", "3524249", "189963073", "189963091", "189963847", "189968887", "189969319", "189969337", "1394194181", "1394194481", "1394194561", "1394197381", "1394199221", "1394199241", "10246935931", "10246936019", "10246936481", "75370121689", "75370121857", "75370122409" ]
[ "nonn" ]
27
0
5
[ "A000040", "A000720", "A048891", "A360277" ]
null
Najeem Ziauddin, Feb 01 2023
2023-02-09T10:39:22
oeisdata/seq/A360/A360277.seq
f2272eac9ddf6bcae06d87e957202d7c
A360278
Determinant of the matrix [L(j+k)+d(j,k)]_{1<=j,k<=n}, where L(n) denotes the Lucas number A000032(n), and d(j,k) is 1 or 0 according as j = k or not.
[ "4", "16", "44", "121", "319", "841", "2204", "5776", "15124", "39601", "103679", "271441", "710644", "1860496", "4870844", "12752041", "33385279", "87403801", "228826124", "599074576", "1568397604", "4106118241", "10749957119", "28143753121", "73681302244", "192900153616", "505019158604", "1322157322201", "3461452807999", "9062201101801", "23725150497404", "62113250390416", "162614600673844", "425730551631121", "1114577054219519" ]
[ "nonn" ]
8
0
5
[ "A000032", "A000045", "A360278" ]
null
Zhi-Wei Sun, Feb 01 2023
2023-02-01T10:23:38
oeisdata/seq/A360/A360278.seq
a2e1e75e8486db13e3d8c228419da756
A360279
Decimal expansion of a constant related to the asymptotics of A302702.
[ "2", "1", "2", "4", "6", "0", "6", "5", "8", "3", "6", "2", "4", "2", "8", "9", "7", "9", "1", "8", "2", "7", "8", "8", "2", "5", "7", "4", "6", "9", "8", "9", "2", "4", "1", "7", "1", "6", "8", "6", "2", "5", "9", "6", "6", "4", "0", "5", "1", "0", "9", "0", "7", "2", "3", "1", "1", "2", "0", "8", "2", "0", "1", "8", "3", "1", "6", "9", "2", "8", "8", "6" ]
[ "nonn", "cons" ]
11
0
5
[ "A302702", "A302703", "A360231", "A360234", "A360235", "A360236", "A360237", "A360279" ]
null
Vaclav Kotesovec, Feb 01 2023
2023-02-05T03:17:08
oeisdata/seq/A360/A360279.seq
c0a9f449c29ce96045f5eeaed4df6503
A360280
Squares that are the hypotenuse of a primitive Pythagorean triangle.
[ "25", "169", "289", "625", "841", "1369", "1681", "2809", "3721", "4225", "5329", "7225", "7921", "9409", "10201", "11881", "12769", "15625", "18769", "21025", "22201", "24649", "28561", "29929", "32761", "34225", "37249", "38809", "42025", "48841", "52441", "54289", "58081", "66049", "70225", "72361", "76729", "78961", "83521", "85849", "93025", "97969" ]
[ "nonn" ]
13
0
5
[ "A000290", "A008846", "A020882", "A198436", "A360280" ]
null
Alexandru Petrescu, Feb 01 2023
2023-02-17T21:44:26
oeisdata/seq/A360/A360280.seq
3e1d34b26fbc4eafb420e4fedd0de233
A360281
Lexicographically earliest sequence of distinct positive integers such that for any n > 2, a(n) is a divisor or a multiple of a(n-1) + a(n-2).
[ "1", "2", "3", "5", "4", "9", "13", "11", "6", "17", "23", "8", "31", "39", "7", "46", "53", "33", "43", "19", "62", "27", "89", "29", "59", "22", "81", "103", "92", "15", "107", "61", "12", "73", "85", "79", "41", "10", "51", "122", "173", "295", "18", "313", "331", "14", "69", "83", "38", "121", "159", "20", "179", "199", "21", "44", "65", "109", "58", "167", "25", "16", "82", "49" ]
[ "nonn" ]
14
0
5
[ "A085947", "A328444", "A332301", "A360281" ]
null
Rémy Sigrist, Feb 01 2023
2024-07-21T11:36:25
oeisdata/seq/A360/A360281.seq
c85b591352c7057826f958cf0e13fc24
A360282
Triangle read by rows. T(n, k) = (1/2) * binomial(2*(n - k + 1), n - k + 1) * binomial(2*n - k, k - 1) for n > 0, T(0, 0) = 1.
[ "1", "0", "1", "0", "3", "2", "0", "10", "12", "3", "0", "35", "60", "30", "4", "0", "126", "280", "210", "60", "5", "0", "462", "1260", "1260", "560", "105", "6", "0", "1716", "5544", "6930", "4200", "1260", "168", "7", "0", "6435", "24024", "36036", "27720", "11550", "2520", "252", "8" ]
[ "nonn", "tabl" ]
16
0
5
[ "A001700", "A053123", "A088218", "A135503", "A172431", "A182626", "A360282", "A360546" ]
null
Peter Luschny, Feb 11 2023
2023-02-14T03:51:51
oeisdata/seq/A360/A360282.seq
4491a9077ccf3858fc14d4a328b08afe
A360283
a(n) = lcm({n! * binomial(n, k) for k = 0..n}).
[ "1", "1", "4", "18", "288", "1200", "43200", "529200", "11289600", "91445760", "9144576000", "92207808000", "13277924352000", "160283515392000", "2094371267788800", "58904191906560000", "15079473128079360000", "242109318556385280000", "78443419212268830720000", "1415903716781452394496000" ]
[ "nonn" ]
11
0
5
[ "A002397", "A003418", "A005722", "A021012", "A196347", "A360283" ]
null
Peter Luschny, Feb 14 2023
2023-02-15T09:41:38
oeisdata/seq/A360/A360283.seq
24f566ff4a2943ed8351793cf4af83d7
A360284
Least integer nu such that the first zero of the Bessel j-function of index nu is at least nu + n.
[ "0", "2", "7", "16", "29", "48", "73", "106", "148", "199", "260", "333", "417", "515", "627", "754", "897", "1057", "1234", "1431", "1647", "1884", "2142", "2423", "2727", "3056", "3410", "3791", "4198", "4634", "5099", "5594", "6120", "6678", "7268", "7893", "8552", "9247", "9979", "10748", "11555", "12402", "13290" ]
[ "nonn" ]
8
0
5
null
null
Charles R Greathouse IV, Feb 01 2023
2023-02-01T23:04:45
oeisdata/seq/A360/A360284.seq
d60ad2d04508d3807e8ff32c1cb2c84e
A360285
Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which no two elements are coprime; n >= 0, 0 <= k <= floor(n/2) + [n=1].
[ "1", "1", "1", "1", "2", "1", "3", "1", "4", "1", "1", "5", "1", "1", "6", "4", "1", "1", "7", "4", "1", "1", "8", "7", "4", "1", "1", "9", "9", "5", "1", "1", "10", "14", "11", "5", "1", "1", "11", "14", "11", "5", "1", "1", "12", "21", "24", "16", "6", "1", "1", "13", "21", "24", "16", "6", "1", "1", "14", "28", "39", "36", "21", "7", "1", "1", "15", "34", "48", "41", "22", "7", "1", "1", "16", "41", "69", "76", "57", "28", "8", "1" ]
[ "nonn", "tabf" ]
18
0
5
[ "A056171", "A355146", "A360285" ]
null
Marcel K. Goh, Feb 01 2023
2023-10-23T17:39:36
oeisdata/seq/A360/A360285.seq
72445bbdcb5a18b3fa27e7cc365b7869
A360286
Irregular triangle read by rows where row n is the lexicographically earliest sequence of visits, taking steps by 1, around a circle of vertices 1..n where the numbers of visits to the vertices are 1..n in some order.
[ "1", "1", "2", "1", "1", "2", "1", "2", "1", "3", "1", "2", "1", "2", "1", "2", "1", "4", "3", "4", "1", "2", "1", "2", "1", "2", "1", "2", "1", "5", "4", "3", "4", "3", "4", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "6", "5", "4", "3", "4", "3", "4", "3", "4", "5", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "7", "6", "5", "4", "3", "4", "3", "4", "3", "4", "3", "4", "5", "6", "5" ]
[ "nonn", "tabf" ]
48
0
5
[ "A000217", "A360286" ]
null
Tamas Sandor Nagy, Feb 01 2023
2023-03-01T23:19:44
oeisdata/seq/A360/A360286.seq
453b94c297737025d45c028adba6a327
A360287
a(n) is the concatenation of the positions of 1-bits in the binary expansion of the Gray code for n, when 1 is the rightmost position; a(0) = 0.
[ "0", "1", "12", "2", "23", "123", "13", "3", "34", "134", "1234", "234", "24", "124", "14", "4", "45", "145", "1245", "245", "2345", "12345", "1345", "345", "35", "135", "1235", "235", "25", "125", "15", "5", "56", "156", "1256", "256", "2356", "12356", "1356", "356", "3456", "13456", "123456", "23456", "2456", "12456", "1456", "456", "46", "146", "1246", "246" ]
[ "nonn", "look", "base" ]
31
0
5
[ "A000225", "A000975", "A003188", "A007908", "A048794", "A227738", "A360287" ]
null
Alois P. Heinz, Feb 01 2023
2023-02-02T16:46:19
oeisdata/seq/A360/A360287.seq
a9504379e65ccd3b45b12766286d8202
A360288
Number T(n,k) of permutations of [n] whose excedance set is the k-th finite subset of positive integers in standard order; triangle T(n,k), n>=0, 0<=k<=ceiling(2^(n-1))-1, read by rows.
[ "1", "1", "1", "1", "1", "3", "1", "1", "1", "7", "3", "7", "1", "3", "1", "1", "1", "15", "7", "31", "3", "17", "7", "15", "1", "7", "3", "7", "1", "3", "1", "1", "1", "31", "15", "115", "7", "69", "31", "115", "3", "37", "17", "69", "7", "37", "15", "31", "1", "15", "7", "31", "3", "17", "7", "15", "1", "7", "3", "7", "1", "3", "1", "1", "1", "63", "31", "391", "15", "245", "115", "675", "7", "145", "69" ]
[ "nonn", "look", "tabf" ]
48
0
5
[ "A000012", "A000027", "A000142", "A000225", "A011782", "A029767", "A048793", "A048794", "A152884", "A263756", "A329369", "A360288", "A360289" ]
null
Alois P. Heinz, Feb 01 2023
2024-12-02T09:30:20
oeisdata/seq/A360/A360288.seq
c02f556e27d7158911bce4b37fe9e04a
A360289
Number T(n,k) of permutations of [n] whose excedance set is the k-th finite subset of positive integers in Gray order; triangle T(n,k), n>=0, 0<=k<=ceiling(2^(n-1))-1, read by rows.
[ "1", "1", "1", "1", "1", "3", "1", "1", "1", "7", "7", "3", "1", "1", "3", "1", "1", "15", "31", "7", "7", "15", "17", "3", "1", "3", "1", "1", "3", "7", "7", "1", "1", "31", "115", "15", "31", "115", "69", "7", "7", "37", "31", "15", "17", "69", "37", "3", "1", "7", "7", "3", "1", "1", "3", "1", "3", "17", "15", "7", "7", "31", "15", "1", "1", "63", "391", "31", "115", "675", "245", "15", "31", "261", "391" ]
[ "nonn", "look", "tabf" ]
33
0
5
[ "A000012", "A000027", "A000142", "A000225", "A003188", "A006068", "A011782", "A152884", "A227738", "A263756", "A360287", "A360288", "A360289" ]
null
Alois P. Heinz, Feb 01 2023
2023-12-09T09:00:08
oeisdata/seq/A360/A360289.seq
0733ef63c7b93dd9b40219987db79c59
A360290
a(n) = Sum_{k=0..floor(n/2)} binomial(n-1-k,k) * binomial(2*n-4*k,n-2*k).
[ "1", "2", "6", "22", "82", "314", "1222", "4814", "19138", "76626", "308550", "1248230", "5069266", "20654602", "84392838", "345659166", "1418769154", "5834283298", "24031706246", "99134911542", "409495076050", "1693539077210", "7011618614342", "29058701620974", "120540377731266", "500443750830962" ]
[ "nonn" ]
13
0
5
[ "A085362", "A360185", "A360290", "A360291", "A360292", "A360293" ]
null
Seiichi Manyama, Feb 01 2023
2023-02-02T10:36:31
oeisdata/seq/A360/A360290.seq
158b2986249a5238dec2c79c41b01909
A360291
a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).
[ "1", "2", "6", "20", "72", "264", "984", "3714", "14148", "54284", "209482", "812196", "3161340", "12345658", "48348522", "189807336", "746740510", "2943359208", "11620961412", "45950375602", "181936110006", "721233025332", "2862271873966", "11370584735100", "45212101270728", "179926167512914" ]
[ "nonn" ]
13
0
5
[ "A085362", "A360186", "A360290", "A360291", "A360292", "A360294" ]
null
Seiichi Manyama, Feb 01 2023
2023-02-03T01:37:31
oeisdata/seq/A360/A360291.seq
25aec394ace56763d0c447a9b65262fa
A360292
a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).
[ "1", "2", "6", "20", "70", "254", "936", "3492", "13150", "49882", "190318", "729576", "2807816", "10841962", "41983588", "162973568", "633994982", "2471010742", "9646981054", "37718873700", "147676286078", "578883674722", "2271704404900", "8923807316892", "35087269756344", "138075819924306" ]
[ "nonn" ]
13
0
5
[ "A085362", "A360290", "A360291", "A360292", "A360295" ]
null
Seiichi Manyama, Feb 01 2023
2023-02-03T01:37:44
oeisdata/seq/A360/A360292.seq
709637bca1e4b59c3dcb0f155daed0d4
A360293
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n-1-k,k) * binomial(2*n-4*k,n-2*k).
[ "1", "2", "6", "18", "58", "194", "662", "2290", "8002", "28178", "99830", "355426", "1270586", "4557682", "16396454", "59135458", "213745922", "774077986", "2808105318", "10202439858", "37118386490", "135210620194", "493082387766", "1799998114770", "6577045868866", "24052649767730", "88031695861590" ]
[ "nonn" ]
8
0
5
[ "A360293", "A360294", "A360295" ]
null
Seiichi Manyama, Feb 01 2023
2023-02-02T10:44:42
oeisdata/seq/A360/A360293.seq
74e967fad0ec454535f830ce600a58d7
A360294
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).
[ "1", "2", "6", "20", "68", "240", "864", "3154", "11628", "43196", "161430", "606228", "2285780", "8647738", "32811378", "124804104", "475748330", "1817005536", "6951390372", "26634502642", "102189927918", "392559063268", "1509684132394", "5811772604124", "22394185567728", "86364110132930", "333329513935842" ]
[ "nonn" ]
12
0
5
[ "A360293", "A360294", "A360295" ]
null
Seiichi Manyama, Feb 01 2023
2023-02-06T18:56:28
oeisdata/seq/A360/A360294.seq
8e04ced55eebee56ab5cf4b2509a5064
A360295
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).
[ "1", "2", "6", "20", "70", "250", "912", "3372", "12590", "47362", "179230", "681528", "2601896", "9966798", "38288420", "147453664", "569092438", "2200577502", "8523612766", "33064771524", "128438624798", "499525018638", "1944918241388", "7580283784548", "29571439970136", "115459524588322", "451157870454298" ]
[ "nonn" ]
13
0
5
[ "A360293", "A360294", "A360295" ]
null
Seiichi Manyama, Feb 01 2023
2023-03-12T10:58:22
oeisdata/seq/A360/A360295.seq
3cd974dd544f44ab938202df6eb50432
A360296
a(1) = 1, and for any n > 1, a(n) is the sum of the terms of the sequence at indices k < n whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.
[ "1", "1", "1", "2", "3", "3", "2", "4", "8", "11", "8", "8", "11", "8", "4", "8", "20", "34", "26", "34", "51", "40", "20", "20", "40", "51", "34", "26", "34", "20", "8", "16", "48", "96", "76", "118", "186", "152", "76", "96", "208", "281", "186", "152", "208", "124", "48", "48", "124", "208", "152", "186", "281", "208", "96", "76", "152", "186", "118", "76", "96", "48", "16", "32" ]
[ "nonn", "look", "base" ]
8
0
5
[ "A165418", "A301983", "A360296" ]
null
Rémy Sigrist, Feb 02 2023
2023-02-02T14:42:44
oeisdata/seq/A360/A360296.seq
6b997024493ccd8814578575f45644f3
A360297
a(n) = minimal positive k such that the sum of the primes prime(n) + prime(n+1) + ... + prime(n+k) is divisible by prime(n+k+1), or -1 if no such k exists.
[ "1", "3", "7", "11", "26", "20", "27", "52", "1650", "142", "53", "168234", "212", "7", "13" ]
[ "nonn", "more", "changed" ]
23
0
5
[ "A000040", "A007504", "A332542", "A332580", "A360297", "A360311", "A360312" ]
null
Scott R. Shannon, Feb 02 2023
2025-04-22T16:26:13
oeisdata/seq/A360/A360297.seq
75af1cb1244dc6bb886ffe2441d6e1b7
A360298
Irregular triangle (an infinite binary tree) read by rows. The tree has root node 1 in row n = 1. For n > 1, each node with value m in row n-1 has a left child with value m / n if n divides m, and a right child with value m * n.
[ "1", "2", "6", "24", "120", "20", "720", "140", "5040", "1120", "630", "40320", "10080", "70", "5670", "4480", "362880", "1008", "100800", "7", "700", "567", "56700", "448", "44800", "36288", "3628800", "11088", "1108800", "77", "7700", "6237", "623700", "4928", "492800", "399168", "39916800", "924", "133056", "92400", "13305600", "924", "92400", "74844", "51975", "7484400", "59136", "5913600", "33264", "4790016", "3326400", "479001600" ]
[ "nonn", "look", "tabf", "easy" ]
12
0
5
[ "A000142", "A008336", "A360173", "A360298", "A360299", "A360300" ]
null
Rémy Sigrist, Feb 02 2023
2023-02-02T14:41:03
oeisdata/seq/A360/A360298.seq
e3257a3c1bfef6e5eae8b33946705162
A360299
a(n) is the number of terms in the n-th row of A360298.
[ "1", "1", "1", "1", "1", "2", "2", "3", "5", "10", "10", "15", "15", "29", "44", "73", "73", "136", "136", "264", "383", "740", "740", "1418", "2440", "4727", "7831", "15154", "15154", "25836", "25836", "46502", "69638", "139276", "240132", "447972", "447972", "880859", "1343707", "2448270", "2448270", "4742231", "4742231", "9309245", "17932278" ]
[ "nonn" ]
5
0
5
[ "A360298", "A360299" ]
null
Rémy Sigrist, Feb 02 2023
2023-02-02T12:47:37
oeisdata/seq/A360/A360299.seq
226cb052ebc1664a739119683a291f45
A360300
a(n) is the least term in the n-th row of A360298.
[ "1", "2", "6", "24", "120", "20", "140", "630", "70", "7", "77", "924", "12012", "858", "5720", "12870", "218790", "12155", "230945", "46189", "969969", "176358", "4056234", "676039", "676039", "104006", "312018", "44574", "1292646", "1077205", "33393355", "66786710", "2203961430", "64822395", "90751353", "90751353", "3357800061" ]
[ "nonn" ]
6
0
5
[ "A008336", "A360298", "A360300" ]
null
Rémy Sigrist, Feb 02 2023
2023-02-02T12:47:31
oeisdata/seq/A360/A360300.seq
19a1fcf976705a00ad9c3bc3b3359699