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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A357501
Length of longest induced cycle in the n X n king graph.
[ "0", "3", "4", "8", "12", "16", "24", "31", "38", "47", "60", "71", "82", "95", "112", "127", "142" ]
[ "nonn", "more" ]
24
1
2
[ "A000982", "A165143", "A357357", "A357501", "A361171" ]
null
Pontus von Brömssen, Oct 01 2022
2023-03-03T20:24:19
oeisdata/seq/A357/A357501.seq
1498976ccc85102386aca140ca2d7f36
A357502
a(n) = ((1 + sqrt(n))^n - (1 - sqrt(n))^n)/(2*sqrt(n)).
[ "1", "2", "6", "20", "80", "342", "1624", "8136", "43776", "246410", "1463264", "9033180", "58200064", "387905182", "2679200640", "19068105488", "139929124864", "1054773505170", "8167509816832", "64795371984420", "526534098026496", "4374163243287398", "37135913476691968", "321727849480560600" ]
[ "nonn", "easy" ]
26
1
2
[ "A099173", "A357502" ]
null
Alexander R. Povolotsky, Oct 01 2022
2022-10-14T16:29:47
oeisdata/seq/A357/A357502.seq
bbbcf8177f5770a5ba452dfcecfaa59b
A357503
a(n) is the hafnian of the 2n X 2n symmetric matrix whose element (i,j) equals abs(i-j).
[ "1", "1", "8", "174", "7360", "512720", "53245824", "7713320944", "1486382446592", "367691598791424", "113570289012090880" ]
[ "nonn", "hard", "more" ]
15
0
3
[ "A049581", "A085750", "A085807", "A094053", "A144216", "A338456", "A357503" ]
null
Stefano Spezia, Oct 01 2022
2023-10-15T09:26:44
oeisdata/seq/A357/A357503.seq
8c563a22f18448868159be6bab7d1759
A357504
Numbers that are the sum of two distinct triangular numbers.
[ "1", "3", "4", "6", "7", "9", "10", "11", "13", "15", "16", "18", "21", "22", "24", "25", "27", "28", "29", "31", "34", "36", "37", "38", "39", "42", "43", "45", "46", "48", "49", "51", "55", "56", "57", "58", "60", "61", "64", "65", "66", "67", "69", "70", "72", "73", "76", "78", "79", "81", "83", "84", "87", "88", "91", "92", "93", "94", "97", "99", "100", "101", "102", "105", "106", "108" ]
[ "nonn", "easy" ]
24
1
2
[ "A000217", "A020756", "A339952", "A357504", "A357505", "A357529" ]
null
Stefano Spezia, Oct 01 2022
2023-06-04T08:56:02
oeisdata/seq/A357/A357504.seq
a618501322ff45d2d06c033bf2c8e01a
A357505
Numbers that are not sum of two distinct triangular numbers.
[ "0", "2", "5", "8", "12", "14", "17", "19", "20", "23", "26", "30", "32", "33", "35", "40", "41", "44", "47", "50", "52", "53", "54", "59", "62", "63", "68", "71", "74", "75", "77", "80", "82", "85", "86", "89", "90", "95", "96", "98", "103", "104", "107", "109", "110", "113", "116", "117", "118", "122", "124", "125", "128", "129", "131", "132", "134", "138", "140", "143", "145", "147" ]
[ "nonn", "easy" ]
16
1
2
[ "A000217", "A020757", "A357504", "A357505", "A357529" ]
null
Stefano Spezia, Oct 01 2022
2023-06-04T08:56:08
oeisdata/seq/A357/A357505.seq
39e4347436a13596ee18cf6c71b12009
A357506
a(n) = A005258(n)^3 * A005258(n-1).
[ "27", "20577", "60353937", "287798988897", "1782634331587527", "13011500170881726987", "106321024671550496694837", "943479109706472533832704097", "8916177779855571182824077866307", "88547154924474394601268826256953077", "915376390434997094066775480671975209017" ]
[ "nonn", "easy" ]
12
1
1
[ "A005258", "A212334", "A339946", "A352655", "A357506", "A357507", "A357508", "A357509" ]
null
Peter Bala, Oct 01 2022
2022-10-13T12:58:13
oeisdata/seq/A357/A357506.seq
e2f6d2ee479c2187d150a8ddf269fdb3
A357507
a(n) = A005259(n)^5 * (A005259(n-1))^7.
[ "3125", "161958718203125", "69598400094777710760545478125", "514885225734532980507136994998009584838203125", "15708056924221066705174364772957342407662356116035885781253125", "1125221282019374727979322420623179115437017599670596496532725068048858642578125" ]
[ "nonn", "easy" ]
9
1
1
[ "A005259", "A212334", "A339946", "A352655", "A357506", "A357507", "A357508", "A357509", "A357567", "A357568", "A357569", "A357956", "A357957", "A357958", "A357959" ]
null
Peter Bala, Oct 01 2022
2022-11-06T12:24:03
oeisdata/seq/A357/A357507.seq
8e58fc21745007263c2d7f5d9cc43e30
A357508
a(n) = binomial(4*n,2*n) - 2*binomial(4*n,n).
[ "-1", "-2", "14", "484", "9230", "153748", "2434964", "37748520", "580043790", "8886848740", "136151207764", "2088760285456", "32108266614164", "494648505828904", "7637081136832840", "118158193386475984", "1831647087068431374", "28444051172077725444", "442429676097305612324" ]
[ "sign", "easy" ]
23
0
2
[ "A001448", "A005810", "A357508", "A357509" ]
null
Peter Bala, Oct 01 2022
2023-03-18T08:49:14
oeisdata/seq/A357/A357508.seq
26ffcddb505d38425b1c6ee95aa9da47
A357509
a(n) = 2*binomial(3*n,n) - 9*binomial(2*n,n).
[ "-7", "-12", "-24", "-12", "360", "3738", "28812", "201672", "1355112", "8936070", "58427226", "380724552", "2479017996", "16151245488", "105359408760", "688338793488", "4504288103784", "29521135717470", "193771020939510", "1273649831269200", "8382448392851610", "55234026483856110", "364347399072847320" ]
[ "sign", "easy" ]
26
0
1
[ "A000984", "A005809", "A268589", "A357508", "A357509" ]
null
Peter Bala, Oct 01 2022
2022-11-07T17:01:03
oeisdata/seq/A357/A357509.seq
84527a5efc02710c5b8c6f095dc5036a
A357510
a(n) = Sum_{k = 0..n} k * binomial(n,k)^2 * binomial(n+k,k)^2.
[ "0", "4", "108", "3144", "95000", "2935020", "92054340", "2918972560", "93330811440", "3003683380020", "97177865060540", "3157623679795992", "102973952434618824", "3368460743291372092", "110480459392323735540", "3631941224582026770720", "119637879389041977365600", "3947968300820696313987780" ]
[ "nonn", "easy" ]
23
0
2
[ "A005259", "A357506", "A357507", "A357510", "A357511", "A357512", "A357513" ]
null
Peter Bala, Oct 01 2022
2022-10-08T10:09:02
oeisdata/seq/A357/A357510.seq
c956e2f811bf88e790186b6bf946530d
A357511
a(n) = numerator of Sum_{k = 1..n} (1/k) * binomial(n,k)^2 * binomial(n+k,k)^2 for n >= 1 with a(0) = 0
[ "0", "4", "54", "2182", "36625", "3591137", "25952409", "4220121443", "206216140401", "47128096330129", "1233722785504429", "364131107601152519", "9971452750252847789", "3611140187389794708497", "102077670374035974509597", "2922063451137950165057717", "169140610796591477659644439" ]
[ "nonn", "easy" ]
15
0
2
[ "A005259", "A357506", "A357507", "A357510", "A357511", "A357512", "A357513" ]
null
Peter Bala, Oct 01 2022
2022-10-08T10:10:04
oeisdata/seq/A357/A357511.seq
509ca5967195203818fd10f246972a6a
A357512
a(n) = Sum_{k = 0..n} k^5 * binomial(n,k)^2 * binomial(n+k,k)^2
[ "0", "4", "1188", "126144", "10040000", "682492500", "41503541940", "2325305113600", "122429236976640", "6140504039242500", "296222848665342500", "13841644170257145792", "629814531655430506944", "28019919084086921883892", "1222770835880665252492500", "52476371578141941012480000", "2219374467089388085650636800" ]
[ "nonn", "easy" ]
16
0
2
[ "A005259", "A007310", "A357510", "A357511", "A357512", "A357513" ]
null
Peter Bala, Oct 02 2022
2022-10-08T10:11:30
oeisdata/seq/A357/A357512.seq
76335aca7e822e633c64f4061ce5f5cc
A357513
a(n) = numerator of Sum_{k = 1..n} (1/k^3) * binomial(n,k)^2 * binomial(n+k,k)^2 for n >= 1 with a(0) = 0
[ "0", "4", "81", "14651", "956875", "1335793103", "697621869", "3929170277787", "573290332967211", "8235727724024089939", "172296487023049395523", "5032311952710217004416313", "114828404520381550476341513", "5947240175728534283432460589661", "144126887537331651710781931325261" ]
[ "nonn", "easy" ]
11
0
2
[ "A005259", "A357510", "A357511", "A357512", "A357513" ]
null
Peter Bala, Oct 02 2022
2022-10-08T10:12:35
oeisdata/seq/A357/A357513.seq
0d566fea574670eb622d5e9f8af78574
A357514
Minimum number of transversals in an orthogonal diagonal Latin square of order n.
[ "1", "0", "0", "8", "15", "0", "23", "16", "132" ]
[ "nonn", "more", "hard" ]
33
1
4
[ "A287644", "A287645", "A344105", "A350585", "A357514" ]
null
Eduard I. Vatutin, Oct 01 2022
2024-10-20T20:13:02
oeisdata/seq/A357/A357514.seq
309533c04b3e2078e0eaea18fca9d6a0
A357515
Smallest positive integer that doubles when the n rightmost digits are shifted to the left end.
[ "105263157894736842", "100502512562814070351758793969849246231155778894472361809045226130653266331658291457286432160804020" ]
[ "nonn", "base" ]
4
1
1
[ "A146088", "A357515" ]
null
Joseph C. Y. Wong, Oct 01 2022
2022-10-02T00:44:15
oeisdata/seq/A357/A357515.seq
fcf405c6d869c3f7d8e118d8d41a09c0
A357516
Number of snake-like polyominoes in an n X n square that start at the NW corner and end at the SE corner and have the maximum length.
[ "1", "2", "6", "20", "2", "64", "44", "512", "28", "4", "64", "520", "480", "6720", "43232", "14400" ]
[ "nonn", "walk", "hard", "more" ]
29
1
2
[ "A331986", "A357234", "A357516" ]
null
Yi Yang, Oct 01 2022
2023-02-28T13:07:11
oeisdata/seq/A357/A357516.seq
118edd6248bc9d36cae1f7a412ca102e
A357517
Primes that are the average of two consecutive primorial numbers A002110 plus one.
[ "5", "19", "270271", "5105101", "103515091681", "3810649312471", "155835500831011", "313986271960080721", "282899575838889614011647241", "113405858671385228324474555982803921209616373612841704311161", "2900763693484834576932132901212043025388720793126978148639249341" ]
[ "nonn" ]
18
1
1
[ "A002110", "A276939", "A357517" ]
null
Nicholas Leonard, Oct 01 2022
2022-11-23T08:56:50
oeisdata/seq/A357/A357517.seq
4143e3270a0d9835a7a116f60df1a6f9
A357518
Unique fixed point of the two-block substitution 00->111, 01->110, 10->101, 11->100.
[ "1", "0", "1", "1", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "1" ]
[ "nonn" ]
13
1
null
[ "A087088", "A354896", "A357448", "A357518" ]
null
Michel Dekking, Oct 02 2022
2022-10-03T08:57:19
oeisdata/seq/A357/A357518.seq
d157d3f210f23c7d357135a28ecd0337
A357519
Number of compositions (ordered partitions) of n into Jacobsthal numbers 1,3,5,11,21,43, ... (A001045).
[ "1", "1", "1", "2", "3", "5", "8", "12", "19", "30", "47", "75", "118", "185", "292", "460", "725", "1143", "1800", "2836", "4469", "7042", "11097", "17485", "27550", "43411", "68403", "107783", "169834", "267606", "421666", "664419", "1046925", "1649640", "2599335", "4095768", "6453698", "10169086", "16023420", "25248087", "39783383" ]
[ "nonn" ]
5
0
4
[ "A001045", "A076739", "A296371", "A357519" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-02T10:29:16
oeisdata/seq/A357/A357519.seq
9a93ad8ef9634e43eb1a4de06c1a1f69
A357520
Expansion of Product_{k>=0} (1 - x^Lucas(k)).
[ "1", "-1", "-1", "0", "0", "2", "0", "-1", "0", "0", "1", "-1", "-1", "1", "0", "1", "-1", "-1", "0", "1", "1", "-1", "0", "0", "0", "1", "-1", "-1", "0", "0", "2", "0", "0", "-1", "-1", "1", "0", "0", "0", "0", "1", "-1", "-1", "0", "0", "2", "0", "-1", "0", "0", "1", "0", "-2", "0", "0", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "-1", "0", "0", "2", "0", "-1", "0", "0", "1", "-1", "-1", "1", "0", "1", "-1", "-1", "1", "0", "0", "-1", "0", "2", "0", "0", "-1", "-1", "1" ]
[ "sign" ]
5
0
6
[ "A000032", "A067593", "A093996", "A357380", "A357382", "A357520" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-02T10:29:12
oeisdata/seq/A357/A357520.seq
3f41468ac416914e011b604e1cd10c8a
A357521
Expansion of Product_{k>=1} (1 - mu(k)*x^k).
[ "1", "-1", "1", "0", "-1", "2", "-3", "3", "-2", "0", "1", "-2", "2", "-2", "1", "-2", "3", "-4", "4", "-2", "0", "2", "-5", "6", "-5", "3", "-2", "1", "-1", "1", "0", "0", "3", "-6", "6", "-5", "4", "0", "-5", "7", "-7", "5", "-2", "2", "0", "-2", "0", "1", "5", "-7", "11", "-14", "11", "-6", "-1", "9", "-12", "8", "-11", "11", "-6", "10", "-13", "8", "-2", "-12", "26", "-26", "24", "-20", "2", "11", "-8", "14", "-15", "9" ]
[ "sign" ]
6
0
6
[ "A008683", "A117208", "A185694", "A292561", "A300663", "A306327", "A357521", "A357524", "A357525" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-02T10:29:08
oeisdata/seq/A357/A357521.seq
96056865685a6bd322a893a0d426e232
A357522
Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539(A063037(1+n)).
[ "0", "1", "2", "3", "6", "5", "4", "7", "8", "11", "10", "9", "16", "17", "18", "15", "12", "13", "14", "19", "32", "23", "22", "21", "24", "31", "28", "27", "26", "29", "30", "25", "20", "33", "42", "49", "48", "43", "44", "47", "50", "41", "34", "37", "38", "53", "52", "39", "36", "35", "40", "51", "46", "45", "74", "75", "84", "65", "58", "59", "64", "85", "86", "63", "60", "57", "66", "83" ]
[ "nonn", "look", "base" ]
12
0
3
[ "A044918", "A056539", "A063037", "A357522", "A357523" ]
null
Rémy Sigrist, Oct 02 2022
2022-10-03T14:55:27
oeisdata/seq/A357/A357522.seq
7cfec58e8809f85834c7f6eb368ed98d
A357523
Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539(A166535(n)); a(0) = 0.
[ "0", "1", "2", "3", "6", "5", "4", "7", "14", "9", "10", "13", "12", "11", "8", "15", "20", "23", "24", "19", "16", "27", "26", "17", "18", "25", "22", "21", "40", "41", "46", "35", "32", "49", "50", "31", "36", "45", "42", "39", "28", "29", "38", "43", "44", "37", "30", "51", "48", "33", "34", "47", "88", "63", "62", "89", "94", "57", "68", "83", "80", "71", "54", "53", "72", "79", "84", "67" ]
[ "nonn", "base" ]
9
0
3
[ "A044918", "A056539", "A166535", "A357522", "A357523" ]
null
Rémy Sigrist, Oct 02 2022
2022-10-03T15:07:54
oeisdata/seq/A357/A357523.seq
0af84f2329c1ccbb6e20e5e6495e440c
A357524
Expansion of Product_{k>=1} 1 / (1 + mu(k)*x^k).
[ "1", "-1", "2", "-1", "2", "0", "1", "2", "0", "3", "0", "4", "1", "4", "2", "4", "4", "4", "5", "6", "6", "6", "8", "8", "10", "9", "11", "12", "13", "14", "17", "17", "20", "19", "23", "24", "28", "27", "30", "34", "34", "40", "41", "47", "48", "50", "56", "62", "64", "71", "72", "80", "85", "91", "99", "104", "113", "112", "128", "135", "147", "153", "159", "176", "180", "196", "210", "220", "233", "240", "264" ]
[ "sign" ]
6
0
3
[ "A008683", "A117211", "A185694", "A300663", "A306327", "A329069", "A357521", "A357524", "A357525" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-02T10:29:04
oeisdata/seq/A357/A357524.seq
e0358a789d9ba81105f0d54e26ee0c42
A357525
Expansion of Product_{k>=1} (1 + mu(k)*x^k).
[ "1", "1", "-1", "-2", "-1", "0", "1", "1", "0", "0", "1", "0", "-2", "-2", "1", "4", "3", "-2", "-4", "-2", "0", "2", "3", "0", "-1", "1", "0", "-3", "-3", "-1", "2", "4", "3", "0", "-2", "-1", "2", "0", "-5", "-3", "3", "3", "0", "-2", "-4", "-2", "4", "5", "3", "3", "1", "-4", "-9", "-8", "3", "11", "6", "0", "-3", "-7", "-4", "2", "-1", "-2", "6", "8", "-2", "-10", "-8", "4", "14", "11", "2", "-6", "-11", "-5" ]
[ "sign" ]
6
0
4
[ "A008683", "A087188", "A117210", "A185694", "A300663", "A306327", "A357521", "A357524", "A357525" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-02T10:28:59
oeisdata/seq/A357/A357525.seq
c2037b9cdf84e76e276548ff99ee5314
A357526
Number of nonnegative integers less than n with the same product of the nonzero decimal digits as n.
[ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "2", "3", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "2", "2", "2", "0", "0", "0", "0", "0", "2", "3", "3", "2", "1", "0", "1", "0", "0", "0", "3", "4", "3", "2", "1", "0", "1", "0", "0", "0", "2", "3", "1", "1", "1", "0", "0", "0", "0", "0", "4", "5", "3", "2", "2", "1", "1", "0", "0", "0", "2", "3", "1", "1", "1", "1", "1", "0", "0", "0", "4", "5", "2", "3", "1", "1", "1", "1", "0", "0", "3" ]
[ "nonn", "base" ]
5
0
11
[ "A051801", "A138471", "A254524", "A338505", "A357526" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-02T13:45:43
oeisdata/seq/A357/A357526.seq
bd1250053e2f3a4f368acff5b3a737ea
A357527
Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539(A044813(n)); a(0) = 0.
[ "0", "1", "2", "4", "3", "5", "7", "6", "8", "12", "11", "10", "9", "13", "23", "18", "20", "22", "15", "21", "16", "19", "17", "14", "24", "36", "29", "33", "35", "26", "34", "32", "31", "27", "30", "28", "25", "37", "55", "44", "47", "49", "52", "54", "39", "53", "51", "40", "50", "41", "48", "46", "42", "45", "43", "38", "56", "82", "63", "68", "76", "79", "81", "58", "69", "73", "80", "78" ]
[ "nonn", "look", "base" ]
12
0
3
[ "A044813", "A044918", "A056539", "A057164", "A357522", "A357523", "A357527" ]
null
Rémy Sigrist, Oct 02 2022
2022-10-03T14:56:04
oeisdata/seq/A357/A357527.seq
af5a3232b5402eefa44acbd2c312a3fa
A357528
Decimal expansion of Sum_{j>=1} 1/A031926(j)^2.
[ "0", "0", "0", "1", "8", "3", "9", "3", "0", "8", "5", "1", "7" ]
[ "nonn", "cons", "hard", "more" ]
20
0
5
[ "A031926", "A085548", "A160910", "A242301", "A356793", "A357059", "A357483", "A357528" ]
null
Artur Jasinski, Oct 02 2022
2022-11-06T09:12:56
oeisdata/seq/A357/A357528.seq
7593bad52d1c8f4b634a519750d75504
A357529
Triangular numbers k such that 2*k cannot be expressed as a sum of two distinct triangular numbers.
[ "0", "1", "6", "10", "15", "45", "55", "66", "91", "120", "136", "231", "276", "300", "406", "435", "496", "561", "595", "630", "741", "780", "820", "861", "1081", "1225", "1326", "1431", "1830", "2016", "2080", "2145", "2211", "2415", "2485", "2701", "2850", "3240", "3321", "3486", "3655", "3916", "4005", "4465", "4560", "4950", "5050", "5356", "5460", "5565" ]
[ "nonn", "easy" ]
19
1
3
[ "A000217", "A002378", "A008851", "A020756", "A020757", "A357504", "A357505", "A357529" ]
null
Stefano Spezia, Oct 02 2022
2022-11-06T14:51:44
oeisdata/seq/A357/A357529.seq
802d9ba611a9754d6674224610c01d6c
A357530
Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539(A031443(n)); a(0) = 0.
[ "0", "1", "2", "3", "4", "11", "8", "7", "6", "9", "12", "5", "10", "13", "14", "45", "41", "31", "18", "38", "28", "21", "22", "27", "37", "36", "26", "23", "20", "29", "39", "17", "32", "42", "46", "35", "25", "24", "19", "30", "40", "16", "33", "43", "47", "15", "34", "44", "48", "49", "170", "165", "150", "115", "54", "161", "146", "111", "58", "136", "101", "68", "81", "88", "123" ]
[ "nonn", "base" ]
10
0
3
[ "A031443", "A044918", "A056539", "A057164", "A357530" ]
null
Rémy Sigrist, Oct 02 2022
2022-10-03T15:08:00
oeisdata/seq/A357/A357530.seq
a303cf26814e3f9e36c7cb3615119794
A357531
Final value obtained by traveling clockwise around a circular array with positions numbered clockwise from 1 to n. Each move consists of traveling clockwise k places, where k is the position at the beginning of the move. The first move begins at position 1. a(n) is the position at the end of the n-th move.
[ "1", "2", "2", "4", "2", "4", "2", "8", "8", "4", "2", "4", "2", "4", "8", "16", "2", "10", "2", "16", "8", "4", "2", "16", "7", "4", "26", "16", "2", "4", "2", "32", "8", "4", "18", "28", "2", "4", "8", "16", "2", "22", "2", "16", "17", "4", "2", "16", "30", "24", "8", "16", "2", "28", "43", "32", "8", "4", "2", "16", "2", "4", "8", "64", "32", "64", "2", "16", "8", "44", "2", "64", "2", "4", "68", "16", "18", "64", "2", "16", "80", "4", "2", "64", "32", "4", "8", "80" ]
[ "nonn", "easy" ]
68
1
2
[ "A015910", "A082495", "A357531", "A358647" ]
null
Moosa Nasir, Nov 19 2022
2024-04-27T09:37:44
oeisdata/seq/A357/A357531.seq
a2e60fcea6b722ef30d573e199127795
A357532
a(n) = Sum_{k=0..floor(n/3)} (n-2*k)!/(n-3*k)!.
[ "1", "1", "1", "2", "3", "4", "7", "12", "19", "34", "63", "112", "211", "414", "799", "1588", "3267", "6706", "13999", "30024", "64723", "141142", "314271", "705724", "1599619", "3685338", "8573167", "20112016", "47804499", "114743614", "277615903", "679057092", "1676636611", "4171532674", "10477002159", "26545428568", "67755344467", "174386589606" ]
[ "nonn", "easy" ]
30
0
4
[ "A072374", "A122852", "A357532", "A357533", "A357570" ]
null
Seiichi Manyama, Nov 19 2022
2022-11-25T06:33:49
oeisdata/seq/A357/A357532.seq
9fa26f4c20986ab8c850efb029901611
A357533
a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/(n-4*k)!.
[ "1", "1", "1", "1", "2", "3", "4", "5", "8", "13", "20", "29", "46", "77", "128", "205", "338", "581", "1012", "1733", "2990", "5293", "9536", "17117", "30778", "56165", "104108", "193621", "360662", "677693", "1289080", "2467373", "4735826", "9142837", "17814308", "34950245", "68835118", "136197581", "271384112", "544302973", "1096578410", "2218459013", "4513377436" ]
[ "nonn", "easy" ]
26
0
5
[ "A072374", "A122852", "A357532", "A357533", "A357570" ]
null
Seiichi Manyama, Nov 19 2022
2022-11-25T06:31:58
oeisdata/seq/A357/A357533.seq
e5a9f1790308adb7a2f16bb66f5a0829
A357534
Number of compositions (ordered partitions) of n into two or more powers of 2.
[ "0", "0", "1", "3", "5", "10", "18", "31", "55", "98", "174", "306", "542", "956", "1690", "2983", "5271", "9310", "16448", "29050", "51318", "90644", "160118", "282826", "499590", "882468", "1558798", "2753448", "4863696", "8591212", "15175514", "26805983", "47350055", "83639030", "147739848", "260967362", "460972286", "814260544", "1438308328" ]
[ "nonn" ]
12
0
4
[ "A023359", "A093659", "A209229", "A357476", "A357534" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-12-26T11:39:47
oeisdata/seq/A357/A357534.seq
829d9d16e580ab78b04fcdd66fc7f15f
A357535
The positive odd numbers x such that x = c^2 - y and +-x = a +- y, where (a,b,c) is a primitive Pythagorean triple (PPT), a is odd and y is an even positive integer.
[ "11", "87", "137", "309", "431", "667", "845", "1427", "1855", "2081", "2129", "2637", "3619", "3651", "3941", "4737", "5051", "5895", "6377", "7871", "9437", "10441", "10521", "11075", "12367", "14221", "15047", "16371", "17141", "17189", "18577", "19307", "20919", "21079", "24431", "24481", "26331" ]
[ "nonn" ]
19
11
1
[ "A020882", "A357535" ]
null
Laura Jokinen, Oct 02 2022
2022-10-19T18:36:59
oeisdata/seq/A357/A357535.seq
de4e57be369a56fd38b03e57ca4adfd2
A357536
Number of colorings of an n X n grid with at most n interchangeable colors under rotational and reflectional symmetry.
[ "1", "4", "490", "22396971", "310449924192274", "1790711048631786194374209", "6372121790133410693083324907292917240", "19460266334869242507206895620675207301301857505549306" ]
[ "nonn" ]
7
1
2
[ "A182044", "A264741", "A264742", "A357536" ]
null
Marko Riedel, Oct 02 2022
2022-10-06T14:42:05
oeisdata/seq/A357/A357536.seq
5715b860bea936f0a58585677cce37ca
A357537
a(n) = 2*A080635(n) if n > 0. a(0) = 1.
[ "1", "2", "2", "6", "18", "78", "378", "2214", "14562", "108702", "897642", "8171766", "81066258", "871695918", "10091490138", "125189658054", "1656458307522", "23288226400062", "346663764078282", "5447099463010326", "90094171024954098", "1564653992673809358", "28467075416816935098", "541467979789775621094" ]
[ "nonn" ]
8
0
2
[ "A080635", "A357537" ]
null
Michael Somos, Oct 02 2022
2022-10-04T07:29:41
oeisdata/seq/A357/A357537.seq
10853e8a608d8b37a77b4dfc1fcde52a
A357538
a(n) = coefficient of x^n in A(x) such that A(x) = 1 + x*(2*A(x)^3 + A(x^3))/3.
[ "1", "1", "2", "6", "21", "78", "308", "1264", "5332", "22994", "100896", "449004", "2021712", "9193509", "42161222", "194768936", "905522052", "4233712140", "19893553120", "93894821200", "444952447944", "2116220266360", "10098086643002", "48330679370584", "231954451580616", "1116046254269592", "5382402925982248" ]
[ "nonn" ]
23
0
3
[ "A000625", "A287211", "A357538", "A375439" ]
null
Paul D. Hanna, Dec 02 2022
2024-08-22T02:06:53
oeisdata/seq/A357/A357538.seq
2b2b8a284b2c6bbdcd118789d8d25cfa
A357539
a(n) = coefficient of x^n/n! in: Sum_{n>=0} ( x*exp(x) )^(n*(n+1)/2).
[ "1", "1", "2", "9", "76", "545", "3966", "47257", "807416", "13431105", "201158650", "2992272041", "55015365252", "1383804654817", "39956273419622", "1127353750507545", "29721911064179056", "748976662158153857", "19509333366569811570", "592071561505183956553", "22102320673776378606140" ]
[ "nonn" ]
21
0
3
null
null
Paul D. Hanna, Dec 05 2022
2022-12-06T07:14:17
oeisdata/seq/A357/A357539.seq
421b498cfdb7887ad2d06f8c9732d72f
A357540
Coefficients T(n,k) of x^(3*n+1)*r^(3*k)/(3*n+1)! in power series S(x,r) = Integral C(x,r)^2 * D(x,r)^2 dx such that C(x,r)^3 - S(x,r)^3 = 1 and D(x,r)^3 - r^3*S(x,r)^3 = 1, as a symmetric triangle read by rows.
[ "1", "4", "4", "160", "800", "160", "20800", "292800", "292800", "20800", "6476800", "191910400", "500121600", "191910400", "6476800", "3946624000", "210590336000", "1091343616000", "1091343616000", "210590336000", "3946624000", "4161608704000", "361556726784000", "3216369361920000", "6333406238720000", "3216369361920000", "361556726784000", "4161608704000", "6974121256960000", "919365914368000000", "12789764316088320000", "42703786876467200000" ]
[ "nonn", "tabl" ]
27
0
2
[ "A104133", "A357540", "A357541", "A357542", "A357543", "A357544", "A357800" ]
null
Paul D. Hanna, Oct 09 2022
2022-10-14T17:55:27
oeisdata/seq/A357/A357540.seq
fc60118128c364d71ea6a9804b2b3c4f
A357541
Coefficients T(n,k) of x^(3*n)*r^(3*k)/(3*n)! in power series C(x,r) = 1 + Integral S(x,r)^2 * D(x,r)^2 dx such that C(x,r)^3 - S(x,r)^3 = 1 and D(x,r)^3 - r^3*S(x,r)^3 = 1, as a triangle read by rows.
[ "1", "2", "0", "40", "120", "0", "3680", "37440", "21600", "0", "880000", "20592000", "38966400", "8553600", "0", "435776000", "19269888000", "79491456000", "57708288000", "6329664000", "0", "386949376000", "28748332800000", "213892766208000", "335872728576000", "123646051584000", "7852204800000", "0", "560034421760000", "64544356546560000", "774705298498560000", "2169194182594560000", "1730103155573760000", "374841224017920000", "15132769090560000", "0" ]
[ "nonn", "tabl" ]
28
0
2
[ "A104134", "A178575", "A357540", "A357541", "A357542", "A357545", "A357801" ]
null
Paul D. Hanna, Oct 09 2022
2023-04-14T09:50:05
oeisdata/seq/A357/A357541.seq
70a45ecca4470402dc1d81d190128227
A357542
Coefficients T(n,k) of x^(3*n)*r^(3*k)/(3*n)! in power series D(x,r) = 1 + r^3 * Integral S(x,r)^2 * D(x,r)^2 dx such that C(x,r)^3 - S(x,r)^3 = 1 and D(x,r)^3 - r^3*S(x,r)^3 = 1, as a triangle read by rows.
[ "1", "0", "2", "0", "120", "40", "0", "21600", "37440", "3680", "0", "8553600", "38966400", "20592000", "880000", "0", "6329664000", "57708288000", "79491456000", "19269888000", "435776000", "0", "7852204800000", "123646051584000", "335872728576000", "213892766208000", "28748332800000", "386949376000", "0", "15132769090560000", "374841224017920000", "1730103155573760000", "2169194182594560000", "774705298498560000", "64544356546560000", "560034421760000" ]
[ "nonn", "tabl" ]
23
0
3
[ "A104134", "A178575", "A357540", "A357541", "A357542", "A357545", "A357802" ]
null
Paul D. Hanna, Oct 09 2022
2022-10-14T17:57:03
oeisdata/seq/A357/A357542.seq
e3a8756391c9adf204822a661bafcab5
A357543
a(n) = (3*n+1)!/(3^n*n!) * Product_{k=1..n} (3*k - 2), for n >= 0.
[ "1", "8", "1120", "627200", "896896000", "2611761152000", "13497581633536000", "112839782456360960000", "1427423248072966144000000", "25979103114927983820800000000", "653945983608967208737177600000000", "22056290135163246016287526092800000000", "971138454651237722097139773865984000000000" ]
[ "nonn" ]
8
0
2
[ "A004117", "A178575", "A357540", "A357543" ]
null
Paul D. Hanna, Oct 10 2022
2022-10-11T00:50:00
oeisdata/seq/A357/A357543.seq
9145b83d1c1c2652d6cefd26db8137a6
A357544
Central terms of triangle A357540: a(n) = A357540(2*n,n).
[ "1", "800", "500121600", "6333406238720000", "588750579021316096000000", "243397196351152229173100544000000", "331908261581281694863434866648678400000000", "1223826698292228823742554320600270140080128000000000", "10588007775487579454220040763957899854099800653824000000000000" ]
[ "nonn" ]
7
0
2
[ "A357540", "A357544" ]
null
Paul D. Hanna, Oct 10 2022
2022-10-11T00:50:09
oeisdata/seq/A357/A357544.seq
a6a7c1da747b780385ecd771b8e290b3
A357545
Central terms of triangle A357541: a(n) = A357541(2*n,n).
[ "1", "120", "38966400", "335872728576000", "23676862831649280000000", "7884265450248813494550528000000", "9001018126678397460727568113336320000000", "28542885018291526761600709316931461578752000000000", "216619327660243309425808505300579182909935738421248000000000" ]
[ "nonn" ]
6
0
2
[ "A357541", "A357542", "A357545" ]
null
Paul D. Hanna, Oct 10 2022
2022-10-11T00:50:19
oeisdata/seq/A357/A357545.seq
a33992a1195881dc100b7b12d1f5a3d2
A357546
a(n) = coefficient of x^n, n >= 0, in A(x) such that: 2 = Sum_{n=-oo..+oo} x^(2*n) * (1 - x^n)^(2*n) * A(x)^n.
[ "1", "2", "4", "6", "12", "18", "52", "92", "278", "606", "1736", "4378", "11974", "31826", "86592", "234514", "645864", "1763784", "4904844", "13503716", "37762996", "104922104", "294474340", "824706556", "2322523264", "6544002006", "18497507308", "52357115006", "148540658418", "421986604840", "1201221586484" ]
[ "nonn" ]
8
0
2
null
null
Paul D. Hanna, Nov 17 2022
2022-12-03T12:07:40
oeisdata/seq/A357/A357546.seq
104bb9d99783d5d1d5289cd1fbd713dd
A357547
a(n) = coefficient of x^n in A(x) such that: A(x)^2 = A( x^2/(1 - 4*x - 4*x^2) ).
[ "1", "2", "9", "38", "176", "832", "4039", "19938", "99861", "506042", "2590099", "13370898", "69540016", "364028992", "1916585714", "10142059868", "53911982971", "287736310102", "1541243386819", "8282387269058", "44638363790176", "241216694913632", "1306608966475854", "7092980525443588", "38581011402034156" ]
[ "nonn" ]
18
1
2
[ "A264224", "A274483", "A274484", "A357547", "A357548", "A357785" ]
null
Paul D. Hanna, Dec 01 2022
2022-12-04T07:34:08
oeisdata/seq/A357/A357547.seq
ff6a968b97374b627bcd6dca6b0ad645
A357548
a(n) = coefficient of x^n in A(x) where A(x)^2 = A( x^2/(1 - 4*x - 8*x^2) ).
[ "1", "2", "11", "50", "261", "1362", "7344", "40112", "222338", "1245476", "7043605", "40153390", "230518723", "1331576430", "7733934030", "45138530004", "264596552838", "1557101158092", "9195520745412", "54477134410680", "323668083179382", "1928047124332764", "11512382184408072", "68889282756213840" ]
[ "nonn" ]
19
1
2
[ "A264224", "A274483", "A274484", "A357547", "A357548", "A357786" ]
null
Paul D. Hanna, Dec 01 2022
2022-12-04T07:36:01
oeisdata/seq/A357/A357548.seq
66e714aa622502da56650d114260a352
A357549
a(n) = floor( Sum_{k=0..n-1} n^k / (k! * a(k)) ), for n > 0 with a(0) = 1.
[ "1", "1", "3", "5", "9", "17", "30", "52", "91", "161", "285", "503", "889", "1573", "2782", "4920", "8697", "15368", "27146", "47928", "84590", "149246", "263247", "464214", "818445", "1442762", "2543025", "4482001", "7898979", "13920609", "24532535", "43234510", "76195273", "134288583", "236682848", "417170144", "735325596", "1296184444" ]
[ "nonn" ]
13
0
3
[ "A030178", "A357549" ]
null
Paul D. Hanna, Dec 01 2022
2022-12-04T13:24:00
oeisdata/seq/A357/A357549.seq
1be894af76102c77e6ea223dff60f7c7
A357550
a(n) = coefficient of x^(2*n-1)/(2*n-1)! in the expansion of the odd function S(x) defined by: S(x) = Integral Product_{n>=1} C(n,x)^(2*n-1) dx, where C(n,x) = (1 - S(x)^(2*n))^(1/(2*n)) for n >= 1.
[ "1", "-1", "-17", "137", "13009", "3098111", "-499973633", "13063051433", "-12602400051359", "1142264265564479", "4900244939751731023", "-1617265022962564577143", "-876540661492989775332431", "772526162637086182379155391", "-84757568544981649947240558113", "-969537581289651588574578501447127" ]
[ "sign" ]
13
1
3
[ "A357228", "A357230", "A357550", "A357551" ]
null
Paul D. Hanna, Oct 02 2022
2022-12-03T12:01:38
oeisdata/seq/A357/A357550.seq
db7c003d7917a865153bfdad40cb785c
A357551
a(n) = coefficient of x^(2*n)/(2*n)! in the expansion of the even function C(x) = sqrt(1 - S(x)^2) where S(x) is defined by A357550.
[ "1", "-1", "1", "107", "913", "-131449", "-46887791", "4109309363", "406392278497", "295047521858639", "5615320767861601", "-121434328185686247493", "13788915057049470673393", "30743837939769538654859351", "-10050889695209166245600514191", "-2332393553453526728340631941757" ]
[ "sign" ]
12
0
4
[ "A357231", "A357550", "A357551" ]
null
Paul D. Hanna, Oct 04 2022
2022-12-03T12:03:38
oeisdata/seq/A357/A357551.seq
ff8c68cec504406a987ca8b35b2f067d
A357552
a(n) = sigma(n) * binomial(2*n-1,n), for n >= 1.
[ "1", "9", "40", "245", "756", "5544", "13728", "96525", "316030", "1662804", "4232592", "37858184", "72804200", "481399200", "1861410240", "9316746045", "21002455980", "176965138350", "353452638000", "2894777105220", "8612125991040", "37873781346960", "98801168731200", "967428110493000", "1959364399785156" ]
[ "nonn" ]
13
1
2
[ "A000203", "A001700", "A156305", "A158267", "A225528", "A357552" ]
null
Paul D. Hanna, Nov 14 2022
2022-11-19T21:06:25
oeisdata/seq/A357/A357552.seq
9076e6bab394843dbd1bd2ed32802806
A357553
a(n) = A000045(n)*A000045(n+1) mod A000032(n).
[ "0", "0", "2", "2", "1", "7", "14", "12", "9", "46", "98", "80", "64", "313", "674", "546", "441", "2143", "4622", "3740", "3025", "14686", "31682", "25632", "20736", "100657", "217154", "175682", "142129", "689911", "1488398", "1204140", "974169", "4728718", "10201634", "8253296", "6677056", "32411113", "69923042", "56568930", "45765225", "222149071", "479259662", "387729212" ]
[ "nonn" ]
17
0
3
[ "A000032", "A000045", "A333599", "A347861", "A357553" ]
null
J. M. Bergot and Robert Israel, Oct 02 2022
2022-10-12T08:57:56
oeisdata/seq/A357/A357553.seq
0ebda57c94932b7049f8e97231b52d69
A357554
Triangular array read by rows. For T(n,k) where 1 <= k <= n, start with x = k and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared, then that is T(n,k).
[ "1", "1", "2", "1", "2", "3", "1", "2", "2", "4", "1", "3", "3", "3", "5", "1", "2", "3", "3", "2", "6", "1", "4", "3", "4", "3", "4", "7", "1", "2", "4", "4", "4", "4", "2", "8", "1", "5", "3", "3", "5", "3", "3", "5", "9", "1", "2", "4", "4", "5", "5", "4", "4", "2", "10", "1", "6", "3", "5", "5", "6", "5", "5", "3", "6", "11", "1", "2", "3", "4", "4", "6", "6", "4", "4", "3", "2", "12", "1", "7", "5", "4", "5", "5", "7", "5", "5", "4", "5", "7", "13" ]
[ "nonn", "tabl", "look" ]
33
1
3
[ "A357554", "A357610" ]
null
J. M. Bergot and Robert Israel, Oct 02 2022
2022-10-16T16:35:37
oeisdata/seq/A357/A357554.seq
e624ecd4d6e7f8c418fb0815d8b76709
A357555
a(n) is the numerator of Sum_{d|n} (-1)^(d+1) / d^2.
[ "1", "3", "10", "11", "26", "5", "50", "43", "91", "39", "122", "55", "170", "75", "52", "171", "290", "91", "362", "143", "500", "183", "530", "215", "651", "255", "820", "275", "842", "13", "962", "683", "1220", "435", "52", "1001", "1370", "543", "1700", "559", "1682", "125", "1850", "61", "2366", "795", "2210", "95", "2451", "1953", "2900", "935", "2810", "205", "3172" ]
[ "nonn", "frac" ]
10
1
2
[ "A017667", "A064027", "A098987", "A119682", "A321543", "A357555", "A357556" ]
null
Ilya Gutkovskiy, Oct 03 2022
2022-10-08T15:11:12
oeisdata/seq/A357/A357555.seq
fab026c3ce698b4d657ab9e5490a29d1
A357556
a(n) is the denominator of Sum_{d|n} (-1)^(d+1) / d^2.
[ "1", "4", "9", "16", "25", "6", "49", "64", "81", "50", "121", "72", "169", "98", "45", "256", "289", "108", "361", "200", "441", "242", "529", "288", "625", "338", "729", "392", "841", "15", "961", "1024", "1089", "578", "49", "1296", "1369", "722", "1521", "800", "1681", "147", "1849", "88", "2025", "1058", "2209", "128", "2401", "2500", "2601", "1352", "2809", "243", "3025" ]
[ "nonn", "frac" ]
9
1
2
[ "A017668", "A064027", "A098988", "A321543", "A334580", "A357555", "A357556" ]
null
Ilya Gutkovskiy, Oct 03 2022
2022-10-08T15:11:16
oeisdata/seq/A357/A357556.seq
a66688a7342f6733e5d0ea3c9ce08979
A357557
a(n) is the numerator of the coefficient c in the polynomial of the form y(x)=x^n+c such that starting with y(x)=x for n=1 each polynomial is C-1 continuous with the previous one.
[ "0", "1", "43", "3481", "12647597", "380547619", "340607106994117", "23867104301800579837", "13408353860832026243555117", "43926321999197203038889578577", "13055436009603783636664151666161626100547", "6766346844526064783736339920897644104961" ]
[ "nonn", "frac" ]
24
1
3
[ "A061464", "A357557" ]
null
Inigo Quilez, Oct 03 2022
2022-10-18T13:33:12
oeisdata/seq/A357/A357557.seq
f455bbf768d1236c5296553eb57c35cb
A357558
a(n) = Sum_{k = 0..n} (-1)^(n+k)*k*binomial(n,k)*binomial(n+k,k)^2.
[ "0", "4", "54", "648", "7500", "85440", "965202", "10849552", "121566744", "1359160020", "15172321890", "169175039616", "1884704860116", "20982512553912", "233474575117770", "2596777575029280", "28872014164369968", "320917108809011868", "3566175414049854306", "39620770883613043240", "440115513924937822020" ]
[ "nonn", "easy" ]
11
0
2
[ "A005258", "A357510", "A357511", "A357512", "A357513", "A357558", "A357559", "A357560", "A357561" ]
null
Peter Bala, Oct 03 2022
2022-10-08T10:15:01
oeisdata/seq/A357/A357558.seq
ff4d7babe24b52e5dd8e8237130f976c
A357559
a(n) = Sum_{k = 0..n} (-1)^(n+k)*k^3*binomial(n,k)*binomial(n+k,k)^2.
[ "0", "4", "270", "8448", "192000", "3669300", "62952162", "1003770880", "15182515584", "220700443500", "3110529630450", "42769154678976", "576313309494000", "7636526099508852", "99765264496070250", "1287663145631539200", "16446680778536421888", "208154776511034178380", "2613380452317012835386" ]
[ "nonn", "easy" ]
14
0
2
[ "A005258", "A357510", "A357512", "A357558", "A357559", "A357560", "A357561" ]
null
Peter Bala, Oct 04 2022
2023-06-02T14:40:14
oeisdata/seq/A357/A357559.seq
9797526e78073ec4153745779ca4b0c4
A357560
a(n) = the numerator of ( Sum_{k = 1..n} (-1)^(n+k)*(1/k)*binomial(n,k)* binomial(n+k,k)^2 ).
[ "0", "4", "0", "94", "500", "19262", "50421", "2929583", "25197642", "2007045752", "3634262225", "368738402141", "6908530637021", "852421484283739", "1168833981781025", "56641833705924527", "276827636652242789", "46345946530867053437", "51051733540797155872", "9673584199611903429172" ]
[ "nonn", "easy" ]
10
0
2
[ "A005258", "A357510", "A357511", "A357512", "A357513", "A357558", "A357559", "A357560", "A357561" ]
null
Peter Bala, Oct 04 2022
2022-10-08T10:18:19
oeisdata/seq/A357/A357560.seq
feb3ee62bd1162115d8aa1cfcd7e4cee
A357561
a(n) = the numerator of ( Sum_{k = 1..n} (-1)^(n+k)*(1/k^3)*binomial(n,k)* binomial(n+k,k)^2 ).
[ "0", "4", "-27", "1367", "-15625", "3129353", "-14749", "308477847", "14343020119", "80826490175689", "618729030402659", "6526775794564145231", "52975460244520902439", "965428117884339747694757", "8161435689582967449592663", "70159702295938799645630801", "4897311439674525483507166097", "212741477113936719632186271679919" ]
[ "sign", "easy" ]
13
0
2
[ "A005258", "A357510", "A357511", "A357512", "A357513", "A357558", "A357559", "A357560", "A357561" ]
null
Peter Bala, Oct 04 2022
2022-10-08T10:19:27
oeisdata/seq/A357/A357561.seq
a3dcc0c18e8ba93cb4d6fe1fb026c90e
A357562
a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A356988(n).
[ "0", "1", "0", "1", "0", "1", "2", "1", "0", "1", "2", "3", "2", "1", "0", "1", "2", "3", "4", "5", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "6", "7", "8", "7", "6", "5", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "12", "11", "10", "9", "8", "7", "6", "5", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "20", "19", "18", "17", "16", "15", "14", "13", "12" ]
[ "nonn", "easy" ]
13
2
7
[ "A000045", "A053646", "A356988", "A357562", "A357563", "A357564" ]
null
Peter Bala, Oct 14 2022
2023-03-10T02:21:08
oeisdata/seq/A357/A357562.seq
b707aec94c962ac72b8b7ad04b61ad83
A357563
a(n) = b(n) - 2*b(b(b(n))) for n >= 3, where b(n) = A356988(n).
[ "0", "1", "1", "0", "1", "1", "0", "1", "2", "2", "2", "1", "0", "1", "2", "3", "3", "3", "3", "2", "1", "0", "1", "2", "3", "4", "5", "5", "5", "5", "5", "5", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "6", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "7", "6", "5", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "12", "11", "10", "9", "8", "7", "6", "5", "4", "3", "2" ]
[ "nonn", "easy" ]
10
3
9
[ "A000032", "A000045", "A356988", "A357562", "A357563" ]
null
Peter Bala, Oct 14 2022
2022-10-23T23:35:24
oeisdata/seq/A357/A357563.seq
de2d22310bd081b926457aca3655f760
A357564
a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A006165(n).
[ "0", "1", "2", "1", "2", "3", "4", "3", "2", "3", "4", "5", "6", "7", "8", "7", "6", "5", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "15", "14", "13", "12", "11", "10", "9", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "31", "30", "29", "28", "27", "26", "25", "24", "23", "22", "21", "20", "19", "18", "17", "16", "17", "18", "19", "20", "21", "22", "23" ]
[ "nonn", "easy" ]
8
2
3
[ "A006165", "A357562", "A357564" ]
null
Peter Bala, Oct 15 2022
2022-10-23T23:35:45
oeisdata/seq/A357/A357564.seq
afe19ea5b0d39b90564f9361fb8f563b
A357565
a(n) = 3*Sum_{k = 0..n} binomial(n+k-1,k)^2 + 2*Sum_{k = 0..n} binomial(n+k-1,k)^3.
[ "5", "10", "114", "2926", "109106", "4846260", "234488526", "11913003294", "625130924082", "33590792825200", "1838547540484364", "102135528447552060", "5743779960435245774", "326352202770939600460", "18706076476872783254286", "1080345839256279791104926", "62806507721442655949609010" ]
[ "nonn", "easy" ]
10
0
1
[ "A357565", "A357566", "A357671", "A357672", "A357673", "A357674" ]
null
Peter Bala, Oct 16 2022
2022-10-25T05:16:01
oeisdata/seq/A357/A357565.seq
1287774317c6242446af2b3c7318f597
A357566
a(n) = ( Sum_{k = 0..n} binomial(n+k-1,k)^2 )^3 * ( Sum_{k = 0..n} binomial(n+k-1,k)^3 )^2.
[ "1", "32", "3556224", "4816142496896", "14260946236464636800", "62923492736113950202540032", "355372959542696519903013302282592", "2376354966106399942850054560101358877184", "17973185649572984869873798116070605084766512000", "149319509846904520286037745483655872001727895961600000" ]
[ "nonn", "easy" ]
10
0
2
[ "A357565", "A357566", "A357671", "A357672", "A357673", "A357674" ]
null
Peter Bala, Oct 16 2022
2022-10-25T05:17:27
oeisdata/seq/A357/A357566.seq
d8e58687cd4bd0cdb1bf01998b107e76
A357567
a(n) = 5*A005259(n) - 14*A005258(n).
[ "-9", "-17", "99", "5167", "147491", "3937483", "105834699", "2907476527", "81702447651", "2342097382483", "68273597307599", "2018243113678027", "60365426282638091", "1823553517258576723", "55557712038989195099", "1705170989220937925167", "52672595030914982754851", "1636296525812843554700323" ]
[ "sign", "easy" ]
14
0
1
[ "A005258", "A005259", "A212334", "A352655", "A357506", "A357507", "A357508", "A357509", "A357567", "A357568", "A357569", "A357956", "A357957", "A357958", "A357959", "A357960" ]
null
Peter Bala, Oct 19 2022
2022-11-06T12:24:16
oeisdata/seq/A357/A357567.seq
75f9394bcf3429ae01c5aac4274742c5
A357568
a(n) = 9*binomial(2*n,n)^2 - 8*binomial(3*n,n).
[ "1", "12", "204", "2928", "40140", "547512", "7535472", "105077376", "1484848332", "21237645000", "306972655704", "4477160465856", "65802123629424", "973487343836448", "14483651478207360", "216550246159148928", "3251660678391659724", "49011343741651501800", "741221951008966181160", "11243583961952559386400" ]
[ "nonn", "easy" ]
34
0
2
[ "A000984", "A002894", "A005809", "A357509", "A357567", "A357568", "A357569", "A357955" ]
null
Peter Bala, Oct 21 2022
2024-07-17T09:00:28
oeisdata/seq/A357/A357568.seq
3a1f1cb81f70ce78381b79988d1fc54e
A357569
a(n) = binomial(3*n,n)^2 - 27*binomial(2*n,n).
[ "-26", "-45", "63", "6516", "243135", "9011205", "344597148", "13520945736", "540917244351", "21966327267885", "902702921361813", "37456461969311736", "1566697064604277788", "65973795093057780936", "2794203818388994498200", "118933541228931589568016", "5084343623375039833670079", "218184481964802862563857685" ]
[ "sign", "easy" ]
17
0
1
[ "A000984", "A005809", "A188662", "A357509", "A357567", "A357568", "A357569", "A357955" ]
null
Peter Bala, Oct 21 2022
2024-07-07T21:08:01
oeisdata/seq/A357/A357569.seq
051b860fb029be46b5de8e3f910e9861
A357570
a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/(n-5*k)!.
[ "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "9", "14", "21", "30", "41", "60", "93", "146", "225", "336", "509", "798", "1281", "2060", "3261", "5154", "8273", "13536", "22365", "36806", "60369", "99588", "166301", "280650", "474801", "802424", "1358973", "2317806", "3987185", "6893196", "11933949", "20690738", "36022161", "63107520", "111146141", "196322454", "347412753" ]
[ "nonn", "easy" ]
31
0
6
[ "A072374", "A122852", "A357532", "A357533", "A357570" ]
null
Seiichi Manyama, Nov 19 2022
2023-02-15T09:41:00
oeisdata/seq/A357/A357570.seq
3f35fe51a4d708014dbcca7980531c9f
A357571
The sixth moment of an n X n random +-1 matrix.
[ "1", "1", "32", "1536", "282624", "66846720", "27053752320", "16104538275840", "13681567224299520", "15874223643851489280", "24412997036693834956800", "48514602066025722465484800", "121994703799547846503012761600", "381343447691461317926230740172800", "1459468400650603118890910517244723200" ]
[ "nonn" ]
36
0
3
[ "A052127", "A357571" ]
null
Zelin Lv, Oct 03 2022
2023-04-21T11:08:00
oeisdata/seq/A357/A357571.seq
b4d7437f013801f705cf5a5b30970e7a
A357572
Expansion of e.g.f. sinh(sqrt(3) * (exp(x)-1)) / sqrt(3).
[ "0", "1", "1", "4", "19", "85", "406", "2191", "13105", "84190", "573121", "4127521", "31434184", "252388957", "2126998693", "18740283556", "172134162631", "1644920020417", "16324076578870", "167938152551491", "1787952325142341", "19667748794844550", "223217829954224029", "2610546296216999197" ]
[ "nonn" ]
34
0
4
[ "A024429", "A027710", "A264037", "A357572", "A357598", "A357615", "A357737" ]
null
Seiichi Manyama, Oct 05 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357572.seq
054869a6b1def7c8b3c257249ddef143
A357573
Largest even k such that h(-k) = 2n, where h(D) is the class number of the quadratic field with discriminant D; or 0 if no such k exists.
[ "232", "1012", "1588", "3448", "5272", "8248", "9172", "14008", "21652", "21508", "26548", "32008", "45208", "53188", "57688", "65668", "73588", "85012", "121972", "120712", "117748", "137272", "189352", "162628", "174868", "201268", "194968", "249208", "188248", "332872", "341608", "424708", "370792", "411832", "377512", "539092", "332308", "486088", "369832", "435268", "604948", "667192", "548788", "601528", "596212", "566008", "737752", "795832", "645208", "802888" ]
[ "nonn", "hard" ]
5
1
1
[ "A038552", "A344072", "A357573" ]
null
Jianing Song, Oct 03 2022
2022-10-06T14:43:09
oeisdata/seq/A357/A357573.seq
83ff6f9c5ee342149e432a54d37be097
A357574
a(n) is the maximum number of pairs that sum to a power of 2 in a set of n consecutive odd numbers.
[ "0", "1", "2", "4", "5", "7", "9", "11", "13", "15", "17", "19", "21", "24", "26", "29", "31", "34", "36", "39", "41", "44", "46", "49", "51", "54", "56", "59", "62", "65", "68", "71", "74", "77", "80", "83", "86", "89", "92", "95", "98", "101", "104", "107", "110", "113", "116", "119", "122", "125", "128", "131", "134", "137", "140", "143", "146", "150", "153", "157", "160", "164", "167" ]
[ "nonn" ]
43
1
3
[ "A020515", "A129868", "A274089", "A347301", "A352178", "A357409", "A357574" ]
null
Thomas Scheuerle, Oct 04 2022
2023-03-10T09:10:58
oeisdata/seq/A357/A357574.seq
11ffe1367c5c9dce83b55071df2fad87
A357575
Half area of the convex hull of {(x,y) | x,y integers and x^2 + y^2 <= n^2}.
[ "0", "1", "4", "12", "21", "37", "52", "69", "93", "120", "152", "181", "212", "258", "297", "345", "388", "444", "495", "552", "616", "673", "749", "814", "881", "965", "1046", "1132", "1211", "1301", "1396", "1483", "1589", "1686", "1800", "1907", "2006", "2128", "2235", "2371", "2490", "2607", "2741", "2872", "3020", "3155", "3293", "3442", "3581", "3739" ]
[ "nonn" ]
24
0
3
[ "A292276", "A357575", "A357576" ]
null
Gerhard Kirchner, Oct 04 2022
2022-10-23T20:46:34
oeisdata/seq/A357/A357575.seq
69f303111090ffc8fe230a988f8e1b86
A357576
Half area of the convex hull of {(x,y)| x,y integers and x^2 + y^2 < n^2}.
[ "0", "2", "8", "17", "28", "46", "63", "87", "112", "142", "173", "204", "244", "287", "333", "378", "428", "485", "540", "602", "661", "737", "802", "869", "947", "1030", "1118", "1197", "1278", "1378", "1469", "1575", "1670", "1776", "1889", "1990", "2108", "2219", "2353", "2472", "2587", "2723", "2854", "3002", "3135", "3275", "3424", "3563", "3721" ]
[ "nonn" ]
16
1
2
[ "A000328", "A004144", "A292276", "A357575", "A357576" ]
null
Gerhard Kirchner, Oct 05 2022
2022-10-23T11:27:26
oeisdata/seq/A357/A357576.seq
eae179611a86053dd40534359ed6d5e7
A357577
Least half area of a convex polygon enclosing a circle with radius n and center (0,0) such that all vertex coordinates are integers.
[ "2", "7", "16", "26", "42", "59", "80", "104", "132", "163", "194", "229", "274", "312", "360", "406", "465", "516", "573", "637", "698", "772", "838", "910", "993", "1073", "1158", "1238", "1333", "1425", "1520", "1621", "1719", "1835", "1936", "2043", "2165", "2280", "2405", "2525", "2650", "2782", "2919", "3059", "3195", "3340", "3486", "3632", "3786" ]
[ "nonn" ]
14
1
1
[ "A357575", "A357576", "A357577" ]
null
Gerhard Kirchner, Oct 17 2022
2024-03-02T12:27:58
oeisdata/seq/A357/A357577.seq
0e3d93d8d618257b829e742123e3df5f
A357578
Lexicographically earliest infinite sequence of distinct positive numbers with the property that a(n) is the smallest number not yet in the sequence with a Hamming weight equal to the Hamming weight of the XOR of previous two terms.
[ "1", "2", "3", "4", "7", "5", "8", "11", "6", "13", "14", "9", "19", "21", "10", "31", "22", "12", "25", "26", "17", "28", "35", "63", "37", "38", "18", "41", "47", "20", "55", "42", "15", "44", "49", "23", "50", "52", "24", "56", "16", "33", "67", "69", "34", "59", "70", "95", "73", "74", "36", "61", "76", "27", "62", "81", "111", "79", "32", "119", "87", "64", "29", "91", "82", "40", "93", "94", "48", "103", "107", "65", "84", "88" ]
[ "nonn", "base" ]
24
1
2
[ "A000120", "A357578" ]
null
Nathan Nichols, Oct 04 2022
2022-10-23T23:53:41
oeisdata/seq/A357/A357578.seq
6a1ab7822b0f31535abc9418f2769be6
A357579
Lexicographically earliest sequence of distinct numbers such that no sum of consecutive terms is a square or higher power of an integer.
[ "2", "3", "7", "5", "6", "12", "10", "11", "17", "18", "15", "13", "20", "14", "23", "19", "28", "26", "22", "21", "29", "33", "35", "37", "24", "31", "30", "38", "34", "41", "39", "40", "44", "43", "46", "42", "51", "45", "54", "53", "48", "57", "47", "50", "59", "52", "61", "58", "55", "60", "56", "66", "67", "65", "62", "70", "63", "69", "73", "72", "76", "74", "68", "79" ]
[ "nonn" ]
22
1
1
[ "A254337", "A357579" ]
null
Carl Witthoft, Oct 03 2022
2022-10-23T04:33:00
oeisdata/seq/A357/A357579.seq
300d3ff5881f8fc8b9fca160b2586551
A357580
a(n) = ((1 + sqrt(n))^n - (1 - sqrt(n))^n)/(2*n*sqrt(n)).
[ "1", "1", "2", "5", "16", "57", "232", "1017", "4864", "24641", "133024", "752765", "4476928", "27707513", "178613376", "1191756593", "8231124992", "58598528065", "429868937728", "3239768599221", "25073052286976", "198825601967609", "1614604933769216", "13405327061690025", "113725655719346176" ]
[ "nonn" ]
24
1
3
[ "A099173", "A357502", "A357580" ]
null
Alexander R. Povolotsky, Oct 04 2022
2022-10-14T16:28:48
oeisdata/seq/A357/A357580.seq
3005526eaa14d652abefa8c48e896d10
A357581
Square array read by antidiagonals of numbers whose symmetric representation of sigma consists only of parts that have width 1; column k indicates the number of parts and row n indicates the n-th number in increasing order in each of the columns.
[ "1", "2", "3", "4", "5", "9", "8", "7", "25", "21", "16", "10", "49", "27", "81", "32", "11", "50", "33", "625", "147", "64", "13", "98", "39", "1250", "171", "729", "128", "14", "121", "51", "2401", "207", "15625", "903", "256", "17", "169", "55", "4802", "243", "31250", "987", "3025", "512", "19", "242", "57", "14641", "261", "117649", "1029", "3249", "6875" ]
[ "nonn", "tabl" ]
16
1
2
[ "A000079", "A001248", "A030514", "A030516", "A174905", "A174973", "A237593", "A238443", "A239929", "A241008", "A241010", "A246955", "A247687", "A264102", "A279102", "A280107", "A318843", "A320066", "A320511", "A341969", "A341970", "A341971", "A357581" ]
null
Hartmut F. W. Hoft, Oct 04 2022
2022-10-11T01:01:57
oeisdata/seq/A357/A357581.seq
787b26b0ed12ca8431f8f01693f5dbdf
A357582
a(n) = A061300(n+1)/A061300(n).
[ "1", "2", "6", "30", "154", "1105", "4788", "20677", "216931", "858925", "7105392", "5546059", "2018025900", "1480452337", "3238556831", "107972737", "18425956230000", "4683032671", "14053747110612300", "160436746661", "33809725025123", "15260431896321667", "1583855315457687090000" ]
[ "nonn", "hard" ]
38
0
2
[ "A061300", "A357582" ]
null
J. Lowell, Oct 04 2022
2023-09-12T08:32:46
oeisdata/seq/A357/A357582.seq
233f795f96d6eb895fa5fd5d9789470a
A357583
Triangle read by rows. Convolution triangle of the Bell numbers.
[ "1", "0", "1", "0", "2", "1", "0", "5", "4", "1", "0", "15", "14", "6", "1", "0", "52", "50", "27", "8", "1", "0", "203", "189", "113", "44", "10", "1", "0", "877", "764", "471", "212", "65", "12", "1", "0", "4140", "3311", "2013", "974", "355", "90", "14", "1", "0", "21147", "15378", "8951", "4440", "1790", "550", "119", "16", "1", "0", "115975", "76418", "41745", "20526", "8727", "3027", "805", "152", "18", "1" ]
[ "nonn", "tabl" ]
10
0
5
[ "A000110", "A007311", "A129247", "A357583", "A357584" ]
null
Peter Luschny, Oct 05 2022
2025-04-06T14:53:35
oeisdata/seq/A357/A357583.seq
e4a20bf0c14b8856118f428f72886778
A357584
Central terms of the convolution triangle of the Bell numbers (A357583).
[ "1", "2", "14", "113", "974", "8727", "80261", "752411", "7159478", "68959643", "671110819", "6590605628", "65253543377", "650982447403", "6541146713073", "66186244142493", "674352479717766", "6919081221705819", "71506844832390551", "744627411078964199", "7816971178681880479", "82780294061365989320" ]
[ "nonn" ]
3
0
2
[ "A357583", "A357584" ]
null
Peter Luschny, Oct 05 2022
2022-10-05T17:43:32
oeisdata/seq/A357/A357584.seq
beeb9273426b37e59ffae15e3b33e14b
A357585
Triangle read by rows. Inverse of the convolution triangle of A108524, the number of ordered rooted trees with n generators.
[ "1", "0", "1", "0", "2", "1", "0", "7", "4", "1", "0", "32", "18", "6", "1", "0", "166", "92", "33", "8", "1", "0", "926", "509", "188", "52", "10", "1", "0", "5419", "2964", "1113", "328", "75", "12", "1", "0", "32816", "17890", "6792", "2078", "520", "102", "14", "1", "0", "203902", "110896", "42436", "13312", "3520", "772", "133", "16", "1" ]
[ "nonn", "tabl" ]
8
0
5
[ "A047891", "A105475", "A108524", "A357585" ]
null
Peter Luschny, Oct 08 2022
2022-10-08T07:44:07
oeisdata/seq/A357/A357585.seq
c9cfaeeb1bb0266094306a664bba5b0b
A357586
Triangle read by rows. Convolution triangle of A002467 (number of permutations with fixed points).
[ "1", "0", "1", "0", "1", "1", "0", "4", "2", "1", "0", "15", "9", "3", "1", "0", "76", "38", "15", "4", "1", "0", "455", "198", "70", "22", "5", "1", "0", "3186", "1182", "378", "112", "30", "6", "1", "0", "25487", "8115", "2274", "629", "165", "39", "7", "1", "0", "229384", "63266", "15439", "3840", "965", "230", "49", "8", "1", "0", "2293839", "554656", "117921", "25966", "6006", "1401", "308", "60", "9", "1" ]
[ "nonn", "tabl" ]
6
0
8
[ "A002467", "A357586" ]
null
Peter Luschny, Oct 09 2022
2024-05-22T06:48:39
oeisdata/seq/A357/A357586.seq
dba9a8037400296da7f30192774293ae
A357587
If k > 1 and k divides DedekindPsi(k) then A358015(k)/2 is a term of this sequence.
[ "1", "4", "3", "8", "12", "16", "9", "24", "32", "36", "48", "27", "64", "72", "96", "108", "128", "144", "81", "192", "216", "256", "288", "324", "384", "432", "243", "512", "576", "648", "768", "864", "972", "1024", "1152", "1296", "729", "1536", "1728", "1944", "2048", "2304", "2592", "2916", "3072", "3456", "3888", "4096", "2187", "4608", "5184", "5832", "6144" ]
[ "nonn" ]
12
1
2
[ "A001615", "A003586", "A033845", "A357587", "A358015" ]
null
Peter Luschny, Oct 26 2022
2024-03-12T14:51:24
oeisdata/seq/A357/A357587.seq
7297389933323be78aef555c0dfd0a4f
A357588
The compositional inverse of n -> n^[isprime(n)], where [b] is the Iverson bracket of b.
[ "1", "-2", "5", "-11", "6", "146", "-1295", "7712", "-36937", "141514", "-357676", "-322973", "12078666", "-102218510", "623243991", "-3041134727", "11440387382", "-23657862864", "-95377084665", "1570488584608", "-12255377466362", "72288056416374", "-340793435817068", "1186234942871544", "-1525020468715715" ]
[ "sign" ]
7
1
2
[ "A089026", "A357368", "A357588" ]
null
Peter Luschny, Oct 04 2022
2022-10-05T02:53:51
oeisdata/seq/A357/A357588.seq
7dd410aa100e8c93af7bd9e247442dd0
A357589
a(n) = n - A130312(n).
[ "0", "1", "1", "2", "2", "3", "4", "3", "4", "5", "6", "7", "5", "6", "7", "8", "9", "10", "11", "12", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36" ]
[ "nonn", "easy" ]
21
1
4
[ "A130312", "A183544", "A357589" ]
null
Mikhail Kurkov, Oct 05 2022
2024-06-21T15:23:42
oeisdata/seq/A357/A357589.seq
5e68171f419c951872a2732c3b5e84e1
A357590
Triangular numbers which are products of five distinct primes.
[ "3570", "8778", "9870", "12090", "13530", "20706", "20910", "21945", "24090", "24310", "26565", "33670", "40470", "40755", "47586", "54285", "57630", "57970", "63546", "66430", "69006", "72390", "76245", "87990", "88410", "91806", "92235", "94395", "94830", "98790", "121278", "130305", "132870", "133386", "141778", "148785", "154290", "159330", "163878", "167910" ]
[ "nonn" ]
17
1
1
[ "A000217", "A046387", "A068443", "A128896", "A333771", "A357590" ]
null
Massimo Kofler, Oct 05 2022
2025-01-11T16:25:57
oeisdata/seq/A357/A357590.seq
241dbb9e54acbadcdde71130c1787855
A357591
Expansion of e.g.f. (exp(x) - 1) * tan((exp(x) - 1)/2).
[ "0", "0", "1", "3", "8", "25", "99", "476", "2643", "16575", "116002", "895719", "7554311", "69051034", "679913073", "7174562327", "80765185416", "966076987581", "12235992073975", "163590477924708", "2302288709067167", "34021599945907915", "526690307104399482", "8524372522971447683", "143963947160570293851" ]
[ "nonn" ]
15
0
4
[ "A001469", "A136128", "A357240", "A357591" ]
null
Vaclav Kotesovec, Oct 05 2022
2022-10-05T10:09:18
oeisdata/seq/A357/A357591.seq
632710af364a1eb2e9f81ec4603e0061
A357592
Number of edges of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector.
[ "3", "11", "34", "96", "260", "683", "1757", "4447", "11114", "27493" ]
[ "nonn", "hard", "more" ]
8
1
1
[ "A007070", "A033303", "A357592" ]
null
Alejandro H. Morales, Oct 05 2022
2022-11-19T14:08:00
oeisdata/seq/A357/A357592.seq
ea123f3eea823d14452a653b580a2883
A357593
Number of faces of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector.
[ "8", "26", "88", "298", "1016", "3466", "11832", "40394", "137912", "470858" ]
[ "nonn", "hard", "more" ]
10
1
1
[ "A007070", "A033303", "A357593" ]
null
Alejandro H. Morales, Oct 05 2022
2022-11-19T20:28:44
oeisdata/seq/A357/A357593.seq
d60e8a1f369f93eb98210059b68f6fe4
A357594
Expansion of e.g.f. log(1-x) * tan(log(1-x)/2).
[ "0", "0", "1", "3", "12", "60", "362", "2562", "20820", "191088", "1955020", "22061380", "272197160", "3645227040", "52656804440", "816114251400", "13508168448400", "237805776169600", "4436759277524400", "87445191383773200", "1815460566861236000", "39600109151685600000", "905416958295793788000" ]
[ "nonn" ]
14
0
4
[ "A136128", "A357591", "A357594" ]
null
Seiichi Manyama, Oct 05 2022
2022-10-05T10:09:12
oeisdata/seq/A357/A357594.seq
6be34a4907802b8f2620fd5019f78b77
A357595
Lexicographically earliest infinite sequence of distinct positive integers such that a(n+1) is the least k != j, for which gcd(k, j) > 1; j = n + a(n).
[ "1", "4", "2", "10", "6", "22", "7", "8", "12", "3", "26", "74", "14", "9", "46", "122", "15", "16", "17", "18", "19", "5", "21", "11", "20", "24", "25", "13", "82", "27", "30", "183", "35", "28", "31", "32", "34", "142", "33", "36", "38", "158", "40", "166", "39", "42", "44", "49", "194", "45", "50", "202", "48", "303", "51", "52", "54", "37", "55", "56", "29", "57", "63", "58", "60", "65" ]
[ "nonn" ]
11
1
2
[ "A347113", "A349472", "A357595" ]
null
David James Sycamore, Oct 05 2022
2022-10-21T15:12:14
oeisdata/seq/A357/A357595.seq
33a6b6bd95d0440e2d602c8d40b172bb
A357596
Number of marked chord diagrams (linear words in which each letter appears twice) with n chords, whose intersection graph is distance-hereditary.
[ "1", "1", "3", "15", "105", "923", "9417", "105815", "1267681", "15875631", "205301361" ]
[ "nonn", "more" ]
10
0
3
[ "A277862", "A277869", "A354588", "A357596" ]
null
Christopher-Lloyd Simon, Oct 05 2022
2022-10-08T14:17:03
oeisdata/seq/A357/A357596.seq
c52cd842911885139e403429dcc024f6
A357597
Decimal expansion of real part of zeta'(0, 1-sqrt(2)).
[ "3", "8", "2", "9", "3", "8", "7", "5", "2", "6", "4", "9", "1", "4", "7", "5", "1", "2", "5", "9", "3", "5", "7", "1", "8", "5", "1", "9", "6", "4", "7", "3", "1", "6", "4", "8", "4", "8", "0", "9", "9", "1", "6", "8", "2", "4", "7", "2", "3", "2", "5", "5", "2", "9", "3", "1", "3", "0", "9", "5", "8", "0", "8", "4", "6", "9", "2", "5", "6", "2", "7", "7", "5", "3", "2", "2", "3", "4", "6", "3", "1", "8", "3", "4", "5", "3", "7", "0", "0", "6", "2", "8", "4", "7", "3", "8", "1", "4", "0", "3", "5", "0", "4", "7", "0" ]
[ "cons", "nonn" ]
70
0
1
[ "A324995", "A324996", "A357597" ]
null
Artur Jasinski, Feb 25 2023
2025-02-16T08:34:04
oeisdata/seq/A357/A357597.seq
6004dd64bd247b4513abfc8d7e2f2457
A357598
Expansion of e.g.f. sinh(2 * (exp(x)-1)) / 2.
[ "0", "1", "1", "5", "25", "117", "601", "3509", "22457", "153141", "1105561", "8453557", "68339833", "581495605", "5184047961", "48259748533", "468040609593", "4719817792565", "49396003390489", "535526127566773", "6004124908829177", "69509047405180213", "829801009239621849", "10202835010223731893" ]
[ "nonn" ]
27
0
4
[ "A024429", "A065143", "A078944", "A264037", "A357572", "A357598", "A357599" ]
null
Seiichi Manyama, Oct 05 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357598.seq
f2d0847680f7e00fde2948aeabdfd8a0
A357599
Expansion of e.g.f. sinh(2 * log(1+x)) / 2.
[ "0", "1", "-1", "6", "-30", "180", "-1260", "10080", "-90720", "907200", "-9979200", "119750400", "-1556755200", "21794572800", "-326918592000", "5230697472000", "-88921857024000", "1600593426432000", "-30411275102208000", "608225502044160000", "-12772735542927360000", "281000181944401920000" ]
[ "sign" ]
10
0
4
[ "A001710", "A133799", "A357598", "A357599" ]
null
Seiichi Manyama, Oct 05 2022
2022-10-05T12:35:36
oeisdata/seq/A357/A357599.seq
0b0d75490ad67d4dbe21c0246791e991
A357600
Largest number k such that C(-k) is the cyclic group of order n, where C(D) is the class group of the quadratic field with discriminant D; or 0 if no such k exists.
[ "163", "427", "907", "1555", "2683", "3763", "5923", "5947", "10627", "13843", "15667", "17803", "20563", "30067", "34483", "31243", "37123", "48427", "38707", "58507", "61483", "85507", "90787", "111763", "93307", "103027", "103387", "126043", "166147", "134467", "133387", "164803", "222643", "189883", "210907", "217627", "158923", "289963", "253507" ]
[ "nonn", "hard" ]
18
1
1
[ "A038552", "A344073", "A357600" ]
null
Jianing Song, Oct 05 2022
2022-10-07T09:15:31
oeisdata/seq/A357/A357600.seq
0b584f4092b948371e9d9c9fe0bea7c3