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int64
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2.35k
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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-14 02:38:35
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A360601
E.g.f. satisfies A(x) = exp(x*A(x)^2) / (1-x).
[ "1", "2", "13", "166", "3265", "87306", "2957509", "121400350", "5857287937", "324884241874", "20370279663901", "1424790170536470", "109990236302275201", "9289460282062082266", "852049115732672006101", "84345608594930495005966", "8962937531710834906989313", "1017655033307013508626619554" ]
[ "nonn" ]
59
0
2
[ "A052750", "A352410", "A352448", "A360601", "A360609", "A370875" ]
null
Seiichi Manyama, Mar 05 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360601.seq
14a1eac201adb87b2c1fa0de31adb285
A360602
a(n) = ((2*n + 1)! / n!)^2 / (n + 1).
[ "1", "18", "1200", "176400", "45722880", "18441561600", "10685567692800", "8414884558080000", "8646761377013760000", "11237331085567082496000", "18020592759036666839040000", "34953943088278121445457920000", "80662945588334126412595200000000", "218412210097326433146332774400000000" ]
[ "nonn" ]
16
0
2
[ "A000108", "A000407", "A122747", "A360602" ]
null
Peter Luschny, Feb 16 2023
2023-03-02T02:58:07
oeisdata/seq/A360/A360602.seq
4e7cd4e137b315c27e9621484db7f334
A360603
Triangle read by rows. T(n, k) = A360604(n, k) * A001187(k) for 0 <= k <= n.
[ "1", "0", "1", "0", "1", "1", "0", "2", "2", "4", "0", "8", "6", "12", "38", "0", "64", "32", "48", "152", "728", "0", "1024", "320", "320", "760", "3640", "26704", "0", "32768", "6144", "3840", "6080", "21840", "160224", "1866256", "0", "2097152", "229376", "86016", "85120", "203840", "1121568", "13063792", "251548592" ]
[ "nonn", "tabl" ]
35
0
8
[ "A001187", "A006125", "A053549", "A054592", "A060818", "A095340", "A123903", "A143543", "A275462", "A360603", "A360604", "A360860" ]
null
Peter Luschny, Feb 20 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360603.seq
cf3d50d0acb6f7df21c982bd115395af
A360604
Triangle read by rows. T(n, k) = 2^binomial(n - k, 2) * binomial(n - 1, k - 1).
[ "1", "0", "1", "0", "1", "1", "0", "2", "2", "1", "0", "8", "6", "3", "1", "0", "64", "32", "12", "4", "1", "0", "1024", "320", "80", "20", "5", "1", "0", "32768", "6144", "960", "160", "30", "6", "1", "0", "2097152", "229376", "21504", "2240", "280", "42", "7", "1", "0", "268435456", "16777216", "917504", "57344", "4480", "448", "56", "8", "1" ]
[ "nonn", "tabl" ]
4
0
8
[ "A002378", "A006125", "A006896", "A130809", "A360604" ]
null
Peter Luschny, Feb 23 2023
2023-02-23T08:36:13
oeisdata/seq/A360/A360604.seq
f9b25fd987de7e16bd025a206827aaef
A360605
The polygonal polynomials evaluated at x = -1/2 and normalized with (-2)^n.
[ "0", "1", "0", "1", "0", "-3", "8", "-31", "72", "-195", "448", "-1071", "2416", "-5475", "12120", "-26719", "58232", "-126243", "271824", "-582575", "1242720", "-2640899", "5592360", "-11806239", "24855080", "-52195843", "109362528", "-228667311", "477218512", "-994205475", "2067947128", "-4294967391", "8908080216" ]
[ "sign", "easy" ]
12
0
6
[ "A139600", "A360605", "A360606" ]
null
Peter Luschny, Feb 21 2023
2025-04-16T17:29:41
oeisdata/seq/A360/A360605.seq
a1d23c55316f437e4ced59acb78c9a5b
A360606
The polygonal polynomials evaluated at x = 1/2 and normalized with 2^n.
[ "0", "1", "4", "13", "40", "117", "324", "853", "2152", "5245", "12436", "28845", "65736", "147685", "327940", "721189", "1573192", "3408237", "7340436", "15729085", "33554920", "71303701", "150995524", "318767733", "671089320", "1409286877", "2952790804", "6174016333", "12884902792", "26843546565", "55834575876" ]
[ "nonn", "easy" ]
15
0
3
[ "A139600", "A360605", "A360606" ]
null
Peter Luschny, Feb 13 2023
2025-04-16T17:29:29
oeisdata/seq/A360/A360606.seq
7d3c75e4ffb9eb360ba1fdafa753cb7f
A360607
a(n) = (n + 1/3) * (3*n + 3)! / ((n + 1)!)^3.
[ "2", "120", "3920", "115500", "3279276", "91483392", "2527462080", "69413752980", "1898945262500", "51809303385840", "1410778953118080", "38360293308573600", "1041896542898685600", "28274302212143040000", "766761376923703054080", "20781963787558897929060", "563007692048242597348500", "15246741943087253044446000" ]
[ "nonn" ]
4
0
1
[ "A000027", "A257589", "A360607" ]
null
Peter Luschny, Feb 15 2023
2023-02-15T07:12:11
oeisdata/seq/A360/A360607.seq
3ee9d09be1dc15de0d029566d22b04b8
A360608
Number of solutions to a 4 X n Ring-Ring puzzle on an empty grid.
[ "1", "0", "2", "1", "8", "12", "45", "98", "292", "725", "2004", "5210", "14051", "37126", "99336", "263991", "704622", "1876566", "5005327", "13341292", "35579622", "94866875", "252998042", "674677856", "1799331865", "4798687520", "12798199466", "34133165825", "91035612400", "242799614636", "647572193925", "1727149489058" ]
[ "nonn", "easy" ]
11
0
3
null
null
George Spahn, Feb 13 2023
2023-02-14T16:32:25
oeisdata/seq/A360/A360608.seq
2d5f31964eb6b6db17b56e188e6f78fe
A360609
E.g.f. satisfies A(x) = exp(x*A(x)^3) / (1-x).
[ "1", "2", "17", "313", "9053", "357941", "17975605", "1095604133", "78570635225", "6482415935449", "604889610870881", "62989604872166897", "7241672622495518773", "911048848278644776949", "124497704904842673086285", "18364053909500922198147421", "2908158473059042016441887025" ]
[ "nonn" ]
39
0
2
[ "A052752", "A352410", "A360601", "A360609", "A361182", "A370876" ]
null
Seiichi Manyama, Mar 05 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360609.seq
85dea81265e7d236494f45b8a8c8212f
A360610
Triangle read by rows: T(n,k) is the number of squares of side length k that can be placed inside a square of side length n without overlap, 1 <= k <= n.
[ "1", "4", "1", "9", "1", "1", "16", "4", "1", "1", "25", "4", "1", "1", "1", "36", "9", "4", "1", "1", "1", "49", "9", "4", "1", "1", "1", "1", "64", "16", "4", "4", "1", "1", "1", "1", "81", "16", "9", "4", "1", "1", "1", "1", "1", "100", "25", "9", "4", "4", "1", "1", "1", "1", "1", "121", "25", "9", "4", "4", "1", "1", "1", "1", "1", "1", "144", "36", "16", "9", "4", "4", "1", "1", "1", "1", "1", "1", "169", "36", "16", "9", "4", "4", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "tabl" ]
51
1
2
[ "A000290", "A008794", "A211547", "A222548", "A287392", "A295643", "A360610" ]
null
Torlach Rush, Feb 13 2023
2023-02-19T17:13:14
oeisdata/seq/A360/A360610.seq
c2f018a7ae6e9c078518166cba297b76
A360611
Expansion of Sum_{k>=0} (k * x * (1 + x))^k.
[ "1", "1", "5", "35", "341", "4230", "63844", "1135753", "23273363", "539881365", "13986073419", "400227436252", "12538263892232", "426810214125441", "15687071552060221", "619144491880324087", "26117514728711229877", "1172635546310430028562", "55833864788507320490268" ]
[ "nonn" ]
14
0
3
[ "A355494", "A360592", "A360611" ]
null
Seiichi Manyama, Feb 14 2023
2023-02-18T22:48:57
oeisdata/seq/A360/A360611.seq
758ebfea27708b7e987db93df4eaf84a
A360612
Number of binary operators defined on the finite chain L_n={0,1,...n}, C:L_n^2-> L_n, which are increasing in each argument, and satisfy the boundary conditions C(0,n)=C(n,0)=0 and C(n,n)=n.
[ "1", "14", "805", "208152", "250409016", "1423422089804", "38533696399916432", "4988815527667401921920", "3096067500138473517778378240", "9222307552079662925642825622240000", "131945758198070262889738914466064452265625", "9070830675953705403006049148134626173379375000000" ]
[ "nonn" ]
18
1
2
[ "A008793", "A071095", "A360612" ]
null
Marc Munar, Feb 14 2023
2023-11-18T09:34:24
oeisdata/seq/A360/A360612.seq
d33df66669d50f4c97c22a611a6f5c8d
A360613
Lexicographically earliest sequence of positive integers such that the products of the form a(2*u-1) * a(2*v) with u, v > 0 are all distinct.
[ "1", "1", "2", "3", "4", "5", "7", "8", "9", "11", "13", "15", "14", "17", "18", "19", "23", "24", "25", "29", "26", "31", "28", "33", "36", "37", "41", "40", "43", "47", "46", "49", "50", "51", "52", "53", "59", "55", "61", "57", "63", "64", "67", "71", "73", "79", "81", "83", "82", "85", "86", "87", "88", "89", "91", "93", "92", "95", "97", "101", "100", "103", "107", "109", "113", "111" ]
[ "nonn" ]
19
1
3
[ "A000695", "A062880", "A066724", "A360613", "A360627", "A360628", "A360633" ]
null
Rémy Sigrist, Feb 14 2023
2023-02-25T15:20:01
oeisdata/seq/A360/A360613.seq
1245643451b65e642bd6bd704a9ac159
A360614
Numerator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0.
[ "0", "1", "2", "1", "3", "1", "4", "1", "1", "3", "5", "2", "6", "2", "3", "1", "7", "2", "8", "1", "2", "5", "9", "1", "3", "3", "2", "4", "10", "1", "11", "1", "5", "7", "2", "1", "12", "4", "3", "3", "13", "4", "14", "5", "1", "9", "15", "2", "2", "1", "7", "2", "16", "1", "5", "1", "4", "5", "17", "3", "18", "11", "4", "1", "3", "5", "19", "7", "9", "4", "20", "2", "21", "6", "1", "8", "5", "2", "22", "3", "1", "13", "23", "1", "7", "7", "5", "5", "24", "3", "3", "3", "11", "15", "4", "1", "25", "4", "5", "3" ]
[ "nonn", "frac" ]
16
1
3
[ "A001222", "A056239", "A061395", "A088529", "A088530", "A106529", "A112798", "A124010", "A316413", "A326567", "A326568", "A334201", "A340609", "A340610", "A348551", "A360008", "A360555", "A360556", "A360557", "A360614", "A360615", "A360688", "A366785" ]
null
Gus Wiseman, Feb 19 2023
2023-10-23T11:47:28
oeisdata/seq/A360/A360614.seq
85174646a2cd841ef26fb8b673dcaeea
A360615
Denominator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0.
[ "0", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "3", "1", "1", "2", "4", "1", "3", "1", "1", "1", "2", "1", "2", "2", "1", "3", "3", "1", "1", "1", "5", "2", "2", "1", "2", "1", "1", "1", "4", "1", "3", "1", "3", "1", "2", "1", "5", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "1", "4", "1", "2", "3", "6", "1", "3", "1", "3", "2", "3", "1", "5", "1", "1", "1", "3", "2", "1", "1", "5", "2", "2", "1", "1", "2", "1", "1", "4" ]
[ "nonn", "frac" ]
14
1
4
[ "A001222", "A056239", "A061395", "A088529", "A088530", "A106529", "A112798", "A124010", "A316413", "A326567", "A326568", "A334201", "A340609", "A340610", "A348551", "A360008", "A360555", "A360556", "A360558", "A360614", "A360615" ]
null
Gus Wiseman, Feb 19 2023
2023-02-20T12:25:50
oeisdata/seq/A360/A360615.seq
39fd6d6ecbb29eb680e8581220cd0d6e
A360616
Half the number of prime factors of n (counted with multiplicity, A001222), rounded down.
[ "0", "0", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1", "2", "0", "1", "0", "1", "1", "1", "0", "2", "1", "1", "1", "1", "0", "1", "0", "2", "1", "1", "1", "2", "0", "1", "1", "2", "0", "1", "0", "1", "1", "1", "0", "2", "1", "1", "1", "1", "0", "2", "1", "2", "1", "1", "0", "2", "0", "1", "1", "3", "1", "1", "0", "1", "1", "1", "0", "2", "0", "1", "1", "1", "1", "1", "0", "2", "2", "1", "0", "2", "1", "1", "1" ]
[ "nonn" ]
6
1
16
[ "A000040", "A000302", "A001222", "A001248", "A026424", "A056239", "A112798", "A168645", "A280076", "A347043", "A347044", "A359912", "A360005", "A360006", "A360457", "A360616", "A360617", "A360671", "A360672", "A360673", "A360674", "A360675", "A360676", "A360677", "A360678", "A360679", "A361200", "A361201" ]
null
Gus Wiseman, Mar 08 2023
2023-03-08T23:17:19
oeisdata/seq/A360/A360616.seq
6b4d11bad31983f20f4403cc88e3df2d
A360617
Half the number of prime factors of n (counted with multiplicity, A001222), rounded up.
[ "0", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "3", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "1", "1", "3", "1", "2", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "2", "3", "1", "2", "1", "2", "1", "2", "1", "3", "1", "1", "2", "2", "1", "2", "1", "3", "2", "1", "1", "2", "1", "1", "1" ]
[ "nonn" ]
6
1
8
[ "A000040", "A000302", "A001222", "A001248", "A026424", "A037143", "A056239", "A081294", "A112798", "A168645", "A347043", "A347044", "A359912", "A360005", "A360006", "A360457", "A360616", "A360617", "A360671", "A360672", "A360673", "A360675", "A360676", "A360677", "A360678", "A360679", "A361200", "A361201" ]
null
Gus Wiseman, Mar 08 2023
2023-03-08T23:17:14
oeisdata/seq/A360/A360617.seq
50247721c552880ede9180bf8f13eecd
A360618
Expansion of Sum_{k>=0} (k * x * (1 + k*x))^k.
[ "1", "1", "5", "43", "515", "7950", "150086", "3349945", "86296849", "2519907605", "82249222661", "2967449372028", "117266100841668", "5037282382077353", "233701540415817409", "11645959855678136519", "620389246928233860127", "35181554115178393462386", "2116059351692554708911298" ]
[ "nonn" ]
16
0
3
[ "A072034", "A360592", "A360611", "A360618" ]
null
Seiichi Manyama, Feb 14 2023
2023-02-15T14:02:19
oeisdata/seq/A360/A360618.seq
bca59a90d901af4a0b9c1232f2f17649
A360619
a(n) > n is the smallest integer such that there exist integers n < c < d satisfying n^3 + a(n)^3 = c^3 + d^3.
[ "12", "16", "36", "32", "60", "48", "84", "53", "34", "27", "93", "40", "156", "112", "80", "106", "39", "68", "228", "54", "238", "176", "94", "80", "167", "156", "102", "224", "99", "67", "246", "166", "279", "78", "98", "120", "174", "304", "468", "108", "319", "69", "516", "352", "170", "188", "97", "160", "282", "96", "82", "312", "550", "204", "113", "371", "180", "198", "708", "134", "600" ]
[ "nonn" ]
38
1
1
[ "A001235", "A360427", "A360619" ]
null
Giedrius Alkauskas, Feb 14 2023
2025-01-08T11:38:32
oeisdata/seq/A360/A360619.seq
773b01011141b502edd7ff4cb5ce253a
A360620
Number of basic cyclotomic generating functions of degree n.
[ "1", "1", "3", "4", "10", "12", "27", "33", "68", "82", "154", "189", "350", "417", "728", "874", "1492", "1767", "2937", "3495", "5692" ]
[ "nonn", "more" ]
8
0
3
[ "A360620", "A360621", "A360622" ]
null
Sara Billey, Feb 14 2023
2023-02-14T11:20:40
oeisdata/seq/A360/A360620.seq
ae2b3d851825e2259e4f9005874cd732
A360621
Number of basic unimodal cyclotomic generating functions of degree n.
[ "1", "1", "2", "3", "6", "8", "14", "20", "34", "48", "72", "100", "162", "214", "309", "437", "641", "860", "1205", "1660", "2361" ]
[ "nonn", "more" ]
14
0
3
[ "A360620", "A360621", "A360622" ]
null
Sara Billey, Feb 14 2023
2023-12-30T17:03:37
oeisdata/seq/A360/A360621.seq
340314c690c1448e918693cf1843ee1e
A360622
Number of basic log-concave (with no internal zeros) cyclotomic generating functions of degree n.
[ "1", "1", "2", "3", "5", "7", "12", "16", "26", "35", "53", "70", "109", "142", "217", "285", "418", "548", "799", "1029", "1490" ]
[ "nonn", "more" ]
12
0
3
[ "A360620", "A360621", "A360622" ]
null
Sara Billey, Feb 14 2023
2023-12-30T17:02:46
oeisdata/seq/A360/A360622.seq
e91daa3a87b4ba92084caaffeb0d1648
A360623
Largest k such that the decimal representation of 2^k is missing any n-digit string.
[ "168", "3499", "53992", "653060" ]
[ "nonn", "base", "more" ]
12
1
1
[ "A094776", "A360623", "A360656" ]
null
Hans Havermann, Feb 14 2023
2023-02-26T20:22:55
oeisdata/seq/A360/A360623.seq
245ef884a05b679bd758238c04f4089c
A360624
Number of strong dichotomy patterns in Z/2nZ, i.e., bicolor patterns of Z/2nZ with respect to the action of Aff(Z/2nZ) with trivial isotropy group.
[ "1", "0", "1", "1", "3", "6", "9", "15", "40", "90", "105", "359", "355", "1092", "3007", "2152", "4305", "17826", "15267", "48549", "130839", "170820", "198753", "780645" ]
[ "nonn", "more" ]
14
1
5
null
null
Octavio A. Agustín-Aquino, Feb 14 2023
2023-02-17T14:46:29
oeisdata/seq/A360/A360624.seq
8b7236725ea8a33aaade86af37b2e3a6
A360625
Triangle read by rows: T(n,k) is the k-th Lie-Betti number of a complete graph on n vertices, n >= 1, k >= 0.
[ "1", "1", "1", "2", "2", "1", "1", "3", "8", "12", "8", "3", "1", "1", "4", "20", "56", "84", "90", "84", "56", "20", "4", "1", "1", "5", "40", "176", "440", "835", "1423", "1980", "1980", "1423", "835", "440", "176", "40", "5", "1", "1", "6", "70", "441", "1616", "4600", "11984", "26824", "46800", "63254", "70784", "70784", "63254", "46800", "26824", "11984", "4600", "1616", "441", "70", "6", "1" ]
[ "nonn", "tabf" ]
29
1
4
[ "A360571", "A360572", "A360625" ]
null
Samuel J. Bevins, Feb 14 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360625.seq
a3c28bdb17005aa9a18f4710d0f0f0da
A360626
Number of multisets of nonempty words over binary alphabet where each letter occurs n times.
[ "1", "3", "21", "131", "830", "5066", "30456", "179256", "1038593", "5928071", "33402561", "186021335", "1025162709", "5596047683", "30282832593", "162573152651", "866385400935", "4585861723905", "24120596727003", "126124094912499", "655868112470175", "3393060517486981", "17468543071082489" ]
[ "nonn" ]
18
0
2
[ "A055375", "A359962", "A360626", "A360638" ]
null
Alois P. Heinz, Feb 14 2023
2023-11-17T11:35:14
oeisdata/seq/A360/A360626.seq
77178dcf91daa13d8f1e117267b0d386
A360627
Odd bisection of A360613: a(n) = A360613(2*n-1).
[ "1", "2", "4", "7", "9", "13", "14", "18", "23", "25", "26", "28", "36", "41", "43", "46", "50", "52", "59", "61", "63", "67", "73", "81", "82", "86", "88", "91", "92", "97", "100", "107", "113", "117", "118", "122", "126", "134", "137", "146", "149", "151", "157", "161", "162", "163", "164", "169", "172", "175", "176", "182", "191", "193", "194", "207", "211", "214", "225" ]
[ "nonn" ]
8
1
2
[ "A360613", "A360627", "A360628", "A360633" ]
null
Rémy Sigrist, Feb 14 2023
2023-02-25T08:32:14
oeisdata/seq/A360/A360627.seq
d3009f7a0fe69fa329fbd5ce61587005
A360628
Even bisection of A360613: a(n) = A360613(2*n).
[ "1", "3", "5", "8", "11", "15", "17", "19", "24", "29", "31", "33", "37", "40", "47", "49", "51", "53", "55", "57", "64", "71", "79", "83", "85", "87", "89", "93", "95", "101", "103", "109", "111", "120", "121", "127", "131", "136", "139", "141", "145", "147", "152", "155", "159", "165", "167", "173", "179", "181", "185", "187", "192", "197", "199", "209", "213", "223", "227" ]
[ "nonn" ]
6
1
2
[ "A360613", "A360627", "A360628", "A360633" ]
null
Rémy Sigrist, Feb 14 2023
2023-02-25T08:32:09
oeisdata/seq/A360/A360628.seq
593286ffef0fbb9ee10b75a43d16e298
A360629
Triangle read by rows: T(n,k) is the number of sets of integer-sided rectangular pieces that can tile an n X k rectangle, 1 <= k <= n.
[ "1", "2", "4", "3", "10", "21", "5", "22", "73", "192", "7", "44", "190", "703", "2035", "11", "91", "510", "2287", "8581", "27407", "15", "172", "1196", "6738", "30209", "118461", "399618", "22", "326", "2895", "19160", "102092", "462114" ]
[ "nonn", "tabl", "more" ]
23
1
2
[ "A000041", "A116694", "A224697", "A360451", "A360629", "A360630", "A360631", "A360632" ]
null
Pontus von Brömssen, Feb 14 2023
2025-05-11T14:20:56
oeisdata/seq/A360/A360629.seq
3b3272d34a856326802c4ae86ff6e400
A360630
Number of sets of integer-sided rectangular pieces that can tile an n X n square.
[ "1", "4", "21", "192", "2035", "27407", "399618" ]
[ "nonn", "more" ]
17
1
2
[ "A034295", "A360629", "A360630" ]
null
Pontus von Brömssen, Feb 14 2023
2025-05-11T14:18:02
oeisdata/seq/A360/A360630.seq
21e9fd185176ab4de6b45658d098ec1e
A360631
Number of sets of integer-sided rectangular pieces that can tile a 2 X n rectangle.
[ "1", "2", "4", "10", "22", "44", "91", "172", "326", "595", "1066", "1849", "3204", "5365", "8921", "14581", "23558", "37440", "59127", "91957", "142060", "217015", "328939", "493917", "737249", "1090432", "1603439", "2341094", "3398313", "4900740", "7032809", "10031010", "14241165", "20112575", "28276657", "39566635", "55140425", "76499692", "105731884", "145550924" ]
[ "nonn" ]
19
0
2
[ "A000041", "A360629", "A360631", "A360632" ]
null
Pontus von Brömssen, Feb 14 2023
2025-05-05T15:48:35
oeisdata/seq/A360/A360631.seq
35568c6db04667220a9f2f16dd4ccab3
A360632
Number of sets of integer-sided rectangular pieces that can tile a 3 X n rectangle.
[ "1", "3", "10", "21", "73", "190", "510", "1196", "2895", "6437", "14281", "29840", "62405", "124506", "246383", "473094", "899000", "1665763", "3057894", "5500889", "9808150" ]
[ "nonn", "more" ]
17
0
2
[ "A000041", "A360629", "A360631", "A360632" ]
null
Pontus von Brömssen, Feb 14 2023
2025-05-09T02:58:52
oeisdata/seq/A360/A360632.seq
8c8d8f5a1092c1edea51be71b136bd88
A360633
Square array A(n, k), n, k > 0, read by antidiagonals upwards; A(n, k) = A360613(2*n-1) * A360613(2*k).
[ "1", "2", "3", "4", "6", "5", "7", "12", "10", "8", "9", "21", "20", "16", "11", "13", "27", "35", "32", "22", "15", "14", "39", "45", "56", "44", "30", "17", "18", "42", "65", "72", "77", "60", "34", "19", "23", "54", "70", "104", "99", "105", "68", "38", "24", "25", "69", "90", "112", "143", "135", "119", "76", "48", "29", "26", "75", "115", "144", "154", "195", "153", "133", "96", "58", "31" ]
[ "nonn", "tabl" ]
12
1
2
[ "A249327", "A360613", "A360627", "A360628", "A360633" ]
null
Rémy Sigrist, Feb 14 2023
2023-02-25T15:28:31
oeisdata/seq/A360/A360633.seq
1c1057f63ad795a7612d2a0aaac7e1f1
A360634
Number T(n,k) of sets of nonempty words over binary alphabet with a total of n letters of which k are the first letter; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
[ "1", "1", "1", "1", "3", "1", "2", "6", "6", "2", "2", "11", "16", "11", "2", "3", "18", "37", "37", "18", "3", "4", "28", "73", "100", "73", "28", "4", "5", "42", "133", "228", "228", "133", "42", "5", "6", "61", "227", "470", "593", "470", "227", "61", "6", "8", "86", "370", "899", "1370", "1370", "899", "370", "86", "8", "10", "119", "580", "1617", "2894", "3497", "2894", "1617", "580", "119", "10" ]
[ "nonn", "tabl" ]
26
0
5
[ "A000009", "A055375", "A095944", "A102866", "A200751", "A208741", "A360634", "A360638", "A360650" ]
null
Alois P. Heinz, Feb 14 2023
2023-12-05T19:46:30
oeisdata/seq/A360/A360634.seq
cf56dadcc2a676aeb2ef6d8ef3d6fc8e
A360635
a(n) is the smallest nonnegative integer that satisfies p(a(n)+1) - p(a(n)) >= n, where p denotes the number partition function.
[ "0", "1", "3", "5", "5", "7", "7", "7", "8", "9", "9", "9", "9", "10", "10", "11", "11", "11", "11", "11", "11", "11", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "16", "16", "16", "16", "17", "17" ]
[ "nonn" ]
18
0
3
[ "A000041", "A001477", "A187219", "A360635" ]
null
Stefano Spezia, Feb 14 2023
2023-02-24T02:04:18
oeisdata/seq/A360/A360635.seq
c205e8f1e0f491ae7a4474df26fc6eb2
A360636
Triangle read by rows. T(n, m) = (1/(n + 1)) * C(n + 1, m) * 4^n * C((3*n - m + 1)/2 - 1, n) if n is odd, otherwise (1/(n + 1)) * C(n + 1, m) * C((3*n - m)/2, n) * C(3*n - m, (3*n - m)/2) / C(n - m, (n - m)/2).
[ "1", "2", "2", "10", "16", "6", "64", "140", "96", "20", "462", "1280", "1260", "512", "70", "3584", "12012", "15360", "9240", "2560", "252", "29172", "114688", "180180", "143360", "60060", "12288", "924", "245760", "1108536", "2064384", "2042040", "1146880", "360360", "57344", "3432" ]
[ "nonn", "tabl" ]
25
0
2
[ "A000984", "A078531", "A151403", "A360636" ]
null
Vladimir Kruchinin, Feb 14 2023
2023-02-15T22:42:47
oeisdata/seq/A360/A360636.seq
322a651fb53a4aed0c8b99e7847da703
A360637
Least crossing number of a prime knot with braid index n.
[ "3", "4", "6", "8", "10", "12" ]
[ "nonn", "more" ]
13
2
1
[ "A002863", "A360637" ]
null
Charles R Greathouse IV, Feb 14 2023
2023-02-16T05:15:33
oeisdata/seq/A360/A360637.seq
1ec1b866036c69e0c549699179b925b2
A360638
Number of sets of nonempty words over binary alphabet where each letter occurs n times.
[ "1", "3", "16", "100", "593", "3497", "20316", "116378", "658214", "3679450", "20350028", "111459648", "605060633", "3257784589", "17408647968", "92378535290", "487031130699", "2552197485757", "13298890952222", "68930923717598", "355507581655752", "1824924721216084", "9326440815314046", "47464093855706540" ]
[ "nonn" ]
16
0
2
[ "A080277", "A360626", "A360634", "A360638" ]
null
Alois P. Heinz, Feb 14 2023
2023-12-09T09:00:03
oeisdata/seq/A360/A360638.seq
9625a5218e034396074bc028b5033e2e
A360639
Numbers k such that k and k+2 are both A000120-perfect numbers (A175522).
[ "123", "219", "695", "1261", "1851", "1943", "3543", "5963", "7031", "7613", "7769", "7861", "10081", "11357", "11629", "12083", "13211", "13791", "14185", "15699", "15835", "15929", "16241", "18649", "20197", "20989", "22521", "23449", "23521", "23963", "24461", "27215", "27829", "28263", "28367", "29485", "29651", "30359", "30901", "31803" ]
[ "nonn", "base" ]
14
1
1
[ "A000120", "A093653", "A175522", "A338452", "A360639", "A360640" ]
null
Amiram Eldar, Feb 15 2023
2023-02-16T12:29:57
oeisdata/seq/A360/A360639.seq
9277875c4d25b749be61313574d3cc05
A360640
a(n) is the start of the least run of exactly n consecutive odd numbers that are A000120-perfect numbers (A175522).
[ "25", "123", "31803", "8019811", "130194395" ]
[ "nonn", "base", "more" ]
9
1
1
[ "A000120", "A093653", "A175522", "A360639", "A360640" ]
null
Amiram Eldar, Feb 15 2023
2023-02-19T02:39:49
oeisdata/seq/A360/A360640.seq
a216a13b73dd61ac6257c3461d31e9cc
A360641
Numbers k where A093653(k)/A000120(k) sets a new record.
[ "1", "2", "4", "8", "12", "16", "24", "36", "66", "72", "132", "144", "264", "420", "528", "840", "1026", "1056", "1680", "2052", "4104", "8208", "16416", "32832", "65664", "73920", "84000", "110880", "118800", "131328", "133380", "237600", "263340", "266760", "526680", "533520", "1053360", "1067040", "2106720", "2134080", "3160080", "4213440" ]
[ "nonn", "base" ]
12
1
2
[ "A000120", "A004394", "A005101", "A093653", "A093687", "A175522", "A175526", "A360641", "A360642" ]
null
Amiram Eldar, Feb 15 2023
2023-02-16T12:25:39
oeisdata/seq/A360/A360641.seq
fed1bbad3e9b90a778ac2cd46522bd0f
A360642
a(n) is the least number k such that A093653(k)/A000120(k) = n.
[ "1", "2", "4", "8", "16", "24", "64", "66", "84", "72", "210", "132", "450", "792", "288", "264", "1044", "672", "5328", "528", "1344", "840", "1026", "1056", "4116", "1800", "4128", "2112", "5124", "3780", "6480", "2184", "3360", "8352", "11088", "8448", "4680", "50700", "4200", "4368", "20880", "8280", "13320", "13440", "12420", "4104", "46200", "8736" ]
[ "nonn", "base" ]
11
1
2
[ "A000120", "A000396", "A007539", "A093653", "A093687", "A175522", "A175526", "A360641", "A360642" ]
null
Amiram Eldar, Feb 15 2023
2023-02-16T12:25:49
oeisdata/seq/A360/A360642.seq
b44878d149139fdc273da0d74bca7dc6
A360643
a(n) is the least A000120-perfect number (A175522) whose binary weight (A000120) is n, or 0 if no such number exists.
[ "2", "0", "25", "169", "841", "95", "247", "943", "767", "5999", "6139", "16123", "30655", "90109", "122847", "245695", "522237", "1572591", "1966015", "3932095", "12582651", "28311519", "33423343", "100663023", "133693435", "402128831", "931135479", "1069547515", "1610612607", "11802771447", "12884901567", "25736249279" ]
[ "nonn", "base" ]
9
1
1
[ "A000120", "A093653", "A175522", "A360643" ]
null
Amiram Eldar, Feb 15 2023
2024-01-25T12:35:15
oeisdata/seq/A360/A360643.seq
ee1554e90279f006cee9d1ebf5c692cf
A360644
Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos, 2 X 2 X 1 plates and trominos (L-shaped connection of 3 cubes).
[ "1", "12", "513", "16194", "547543", "18234354", "609298887", "20344385080", "679408772089", "22688284005780", "757662377924917", "25301659203704234", "844933359518672599", "28216027727373068302", "942256839186226313727", "31466085716246304261600", "1050790517091131646143477" ]
[ "nonn" ]
5
0
2
[ "A001045", "A006253", "A033516", "A335559", "A359884", "A359885", "A360064", "A360065", "A360644" ]
null
Gerhard Kirchner, Feb 15 2023
2023-02-16T05:14:31
oeisdata/seq/A360/A360644.seq
b767751fc8ccc887ff02f72ffc1607b2
A360645
Number of 4-dimensional tilings of a 2 X 2 X 2 X n box with 2 X 2 X 1 X 1 plates.
[ "1", "3", "30", "177", "1281", "8520", "58629", "397887", "2715510", "18490533", "126023349", "858595560", "5850498441", "39863005323", "271617783150", "1850725023657", "12610357769721", "85923544106760", "585460036653789", "3989166905015367", "27181111280961990", "185204779320272253" ]
[ "nonn" ]
16
0
2
[ "A001045", "A006253", "A359884", "A360645" ]
null
Gerhard Kirchner, Feb 15 2023
2024-05-28T17:56:52
oeisdata/seq/A360/A360645.seq
1a645b69f3d3ecbaa0f48c7b343493fa
A360646
Square array A(n, k), n, k > 0, read by antidiagonals upwards; A(n, k) = A066208(n) * A066207(k).
[ "1", "2", "3", "4", "6", "7", "5", "12", "14", "9", "8", "15", "28", "18", "13", "10", "24", "35", "36", "26", "19", "11", "30", "56", "45", "52", "38", "21", "16", "33", "70", "72", "65", "76", "42", "27", "17", "48", "77", "90", "104", "95", "84", "54", "29", "20", "51", "112", "99", "130", "152", "105", "108", "58", "37", "22", "60", "119", "144", "143", "190", "168", "135", "116", "74", "39" ]
[ "nonn", "tabl" ]
7
1
2
[ "A066207", "A066208", "A247503", "A248101", "A249327", "A360646" ]
null
Rémy Sigrist, Feb 15 2023
2023-02-16T05:06:19
oeisdata/seq/A360/A360646.seq
1078878221cd87c6cb2de15f28dbae2d
A360647
Expansion of Sum_{k>=0} (k^2 * x * (1 + x))^k.
[ "1", "1", "17", "761", "67739", "10029956", "2226004406", "691381685259", "286255287677425", "152360721379689043", "101358756787489940837", "82408168580060017122144", "80396790074312939684672316", "92691781529853274368541343021" ]
[ "nonn" ]
10
0
3
[ "A323280", "A360611", "A360647" ]
null
Seiichi Manyama, Feb 15 2023
2023-02-16T09:46:44
oeisdata/seq/A360/A360647.seq
7440ea63c88f9259d3fbec92dc90b103
A360648
Fully multiplicative with a(A027697(k)) = A027699(k) and a(A027699(k)) = A027697(k) for any k > 0.
[ "1", "3", "2", "9", "7", "6", "5", "27", "4", "21", "17", "18", "23", "15", "14", "81", "11", "12", "29", "63", "10", "51", "13", "54", "49", "69", "8", "45", "19", "42", "43", "243", "34", "33", "35", "36", "53", "87", "46", "189", "71", "30", "31", "153", "28", "39", "83", "162", "25", "147", "22", "207", "37", "24", "119", "135", "58", "57", "89", "126", "101", "129", "20", "729" ]
[ "nonn", "base", "mult" ]
9
1
2
[ "A027697", "A027699", "A061898", "A341090", "A360648" ]
null
Rémy Sigrist, Feb 15 2023
2023-02-16T05:06:31
oeisdata/seq/A360/A360648.seq
5ac24ff4ce22c823b3be2008a07fa9f0
A360649
The exponents that occur in the greedy representation of 1/2 as a sum of powers of 2/3.
[ "2", "8", "11", "14", "16", "26", "33", "38", "45", "48", "51", "53", "65", "69", "72", "80", "83", "89", "94", "101", "105", "109", "115", "118", "123", "131", "139", "142", "148", "152", "157", "160", "164", "170", "176", "179", "182", "185", "188", "193", "197", "208", "214", "220", "223", "225", "232", "234", "240", "243", "247", "250", "254", "258", "261", "271" ]
[ "nonn" ]
24
1
1
[ "A058840", "A077468", "A360649" ]
null
James Propp, Feb 15 2023
2024-11-04T01:46:10
oeisdata/seq/A360/A360649.seq
e754531aee7d49cf089c0b45b3e91a21
A360650
Number of sets of nonempty words over binary alphabet with a total of n letters of which 2 are the first letter.
[ "0", "0", "1", "6", "16", "37", "73", "133", "227", "370", "580", "881", "1305", "1890", "2687", "3756", "5175", "7037", "9460", "12582", "16577", "21649", "28048", "36070", "46072", "58474", "73778", "92574", "115559", "143551", "177510", "218556", "267997", "327355", "398394", "483162", "584023", "703708", "845361", "1012600", "1209573" ]
[ "nonn" ]
10
0
4
[ "A360634", "A360650" ]
null
Alois P. Heinz, Feb 15 2023
2023-02-15T10:23:08
oeisdata/seq/A360/A360650.seq
8595530f3a8a9b091df9832352ae4160
A360651
Triangle T(n, m) = (n - m + 1)*C(2*n + 1, m)*C(2*n - m + 2, n - m + 1)/(2*n - m + 2).
[ "1", "3", "3", "10", "20", "10", "35", "105", "105", "35", "126", "504", "756", "504", "126", "462", "2310", "4620", "4620", "2310", "462", "1716", "10296", "25740", "34320", "25740", "10296", "1716", "6435", "45045", "135135", "225225", "225225", "135135", "45045", "6435", "24310", "194480", "680680", "1361360", "1701700", "1361360", "680680", "194480", "24310" ]
[ "nonn", "tabl" ]
11
0
2
[ "A001700", "A069720", "A085880", "A360651" ]
null
Vladimir Kruchinin, Feb 15 2023
2023-02-15T15:24:07
oeisdata/seq/A360/A360651.seq
b8979e915291f3d2c0de79577f72859f
A360652
Primes of the form x^2 + 432*y^2.
[ "433", "457", "601", "1657", "1753", "1777", "1801", "2017", "2089", "2113", "2281", "2689", "2833", "2953", "3457", "3889", "4057", "4129", "4153", "4177", "4513", "4657", "4729", "5113", "5209", "5449", "5569", "5737", "5953", "6217", "6361", "6673", "6961", "7057", "7321", "7369", "7537", "7753", "7873", "8353", "8377", "8713", "8761", "8929" ]
[ "nonn" ]
9
1
1
[ "A014752", "A023394", "A229850", "A351332", "A360652" ]
null
Arkadiusz Wesolowski, Feb 15 2023
2023-07-17T10:33:40
oeisdata/seq/A360/A360652.seq
9b2ef525bd0e4d91ab106d8f399f53ea
A360653
Irregular table read by rows; the first row contains the value 1, and for n > 1, the n-th row lists the numbers of the form binomial(m-1, k) such that binomial(m, k) = n.
[ "1", "1", "1", "2", "1", "3", "1", "4", "1", "3", "5", "1", "6", "1", "7", "1", "8", "1", "4", "6", "9", "1", "10", "1", "11", "1", "12", "1", "13", "1", "5", "10", "14", "1", "15", "1", "16", "1", "17", "1", "18", "1", "10", "19", "1", "6", "15", "20", "1", "21", "1", "22", "1", "23", "1", "24", "1", "25", "1", "26", "1", "7", "21", "27", "1", "28", "1", "29", "1", "30", "1", "31", "1", "32", "1", "33", "1", "15", "20", "34" ]
[ "nonn", "tabf" ]
10
1
4
[ "A003016", "A006987", "A007318", "A360653", "A360654", "A360655" ]
null
Rémy Sigrist, Feb 15 2023
2023-02-16T05:06:40
oeisdata/seq/A360/A360653.seq
442e04c3e62118f7956f0a82dc7d2dc8
A360654
Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m, k-1) such that binomial(m, k) = n.
[ "1", "1", "3", "1", "6", "1", "10", "1", "4", "15", "1", "21", "1", "28", "1", "36", "1", "5", "10", "45", "1", "55", "1", "66", "1", "78", "1", "91", "1", "6", "20", "105", "1", "120", "1", "136", "1", "153", "1", "171", "1", "15", "190", "1", "7", "35", "210", "1", "231", "1", "253", "1", "276", "1", "300", "1", "325", "1", "351", "1", "8", "56", "378", "1", "406", "1", "435", "1", "465", "1", "496" ]
[ "nonn", "tabf" ]
10
2
3
[ "A000217", "A007318", "A360653", "A360654", "A360655" ]
null
Rémy Sigrist, Feb 15 2023
2023-02-16T05:06:49
oeisdata/seq/A360/A360654.seq
5d8a31173706a37a136e21b282025218
A360655
Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m+1, k) such that binomial(m, k) = n.
[ "3", "4", "6", "5", "10", "6", "15", "7", "10", "21", "8", "28", "9", "36", "10", "45", "11", "15", "20", "55", "12", "66", "13", "78", "14", "91", "15", "105", "16", "21", "35", "120", "17", "136", "18", "153", "19", "171", "20", "190", "21", "35", "210", "22", "28", "56", "231", "23", "253", "24", "276", "25", "300", "26", "325", "27", "351", "28", "378", "29", "36", "84", "406", "30", "435" ]
[ "nonn", "tabf" ]
6
2
1
[ "A007318", "A360653", "A360654", "A360655" ]
null
Rémy Sigrist, Feb 15 2023
2023-02-16T05:07:02
oeisdata/seq/A360/A360655.seq
93c446e599f6689f9d76dc00cc83414b
A360656
Least k such that the decimal representation of 2^k contains all possible n-digit strings.
[ "68", "975", "16963", "239697", "2994863" ]
[ "nonn", "base", "more" ]
14
1
1
[ "A171744", "A360623", "A360656" ]
null
Hans Havermann, Feb 15 2023
2023-02-26T20:26:57
oeisdata/seq/A360/A360656.seq
5ebad70acad9129610971d5a307e1a80
A360657
Number triangle T associated with 2-Stirling numbers and Lehmer-Comtet numbers (see Comments and Formula section).
[ "1", "0", "1", "0", "2", "1", "0", "9", "5", "1", "0", "64", "37", "9", "1", "0", "625", "369", "97", "14", "1", "0", "7776", "4651", "1275", "205", "20", "1", "0", "117649", "70993", "19981", "3410", "380", "27", "1", "0", "2097152", "1273609", "365001", "64701", "7770", "644", "35", "1", "0", "43046721", "26269505", "7628545", "1388310", "174951", "15834", "1022", "44", "1" ]
[ "nonn", "easy", "tabl" ]
35
0
5
[ "A000007", "A000012", "A000096", "A000169", "A049444", "A055869", "A088956", "A094587", "A143494", "A354794", "A354795", "A360657", "A360753" ]
null
Werner Schulte, Feb 15 2023
2023-12-17T11:22:07
oeisdata/seq/A360/A360657.seq
fff1fb51fcd15aa26c284999aadeacdc
A360658
a(1) = 1; a(n) = -Sum_{k=2..n} k^3 * a(floor(n/k)).
[ "1", "-8", "-35", "-27", "-152", "91", "-252", "-252", "-252", "873", "-458", "-674", "-2871", "216", "3591", "3591", "-1322", "-1322", "-8181", "-9181", "80", "12059", "-108", "-108", "-108", "19665", "19665", "16921", "-7468", "-37843", "-67634", "-67634", "-31697", "12520", "55395", "55395", "4742", "66473", "125792", "125792", "56871", "-26478" ]
[ "sign" ]
85
1
2
[ "A092149", "A336277", "A359478", "A359531", "A360390", "A360658" ]
null
Seiichi Manyama, Apr 01 2023
2023-05-10T04:31:15
oeisdata/seq/A360/A360658.seq
fff9ae57ab0ab03875081aaea1b2fadc
A360659
a(n) is the minimum sum of a completely multiplicative sign sequence of length n.
[ "0", "1", "0", "-1", "0", "-1", "0", "-1", "-2", "-1", "0", "-1", "-2", "-3", "-4", "-3", "-2", "-3", "-4", "-5", "-4", "-5", "-4", "-5", "-6", "-5", "-6", "-7", "-8", "-9", "-8", "-9", "-8", "-7", "-8", "-7", "-6", "-7", "-8", "-7", "-8", "-9", "-10", "-11", "-12", "-13", "-14", "-15", "-14", "-13", "-12", "-13", "-14", "-15", "-14", "-13", "-14", "-15", "-16", "-17", "-18", "-19" ]
[ "sign" ]
72
0
9
[ "A000720", "A002819", "A007913", "A008836", "A360659" ]
null
Bartlomiej Pawlik, Feb 15 2023
2024-06-17T15:31:33
oeisdata/seq/A360/A360659.seq
c768d27f9a91477e9117d446f96437e8
A360660
Number of inequivalent n X n {0,1} matrices modulo permutation of the rows, with exactly n 1's.
[ "1", "1", "4", "20", "133", "1027", "9259", "94033", "1062814", "13176444", "177427145", "2573224238", "39924120823", "658921572675", "11513293227271", "212109149134617", "4105637511110979", "83238756058333277", "1762856698153603049", "38905470655863251479", "892840913430059075405" ]
[ "nonn" ]
45
0
3
[ "A091058", "A091059", "A154323", "A220886", "A246107", "A256070", "A360660", "A360664", "A383073" ]
null
Alois P. Heinz, Feb 15 2023
2025-04-15T14:11:28
oeisdata/seq/A360/A360660.seq
921b7344731847ab0373934c1ea9aa52
A360661
Number of factorizations of n into a prime number of factors > 1.
[ "0", "0", "0", "1", "0", "1", "0", "2", "1", "1", "0", "3", "0", "1", "1", "3", "0", "3", "0", "3", "1", "1", "0", "5", "1", "1", "2", "3", "0", "4", "0", "5", "1", "1", "1", "7", "0", "1", "1", "5", "0", "4", "0", "3", "3", "1", "0", "9", "1", "3", "1", "3", "0", "5", "1", "5", "1", "1", "0", "9", "0", "1", "3", "7", "1", "4", "0", "3", "1", "4", "0", "12", "0", "1", "3", "3", "1", "4", "0", "9", "3", "1", "0", "9", "1", "1", "1", "5", "0", "9", "1", "3", "1", "1", "1", "13", "0", "3", "3", "7" ]
[ "nonn" ]
24
1
8
[ "A001055", "A001248", "A001358", "A006881", "A007304", "A008578", "A030078", "A030514", "A038499", "A054753", "A080258", "A339890", "A360661" ]
null
Ilya Gutkovskiy, Feb 15 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360661.seq
e4788cfbd62f8d93ca1c8f6c3c12104b
A360662
Numbers having more than one representation as the product of at least two consecutive odd integers > 1.
[ "135135", "2110886623587616875", "118810132577324221759073444371080321140625", "262182986027006205192949807157375529898104505103011391412633845449072265625" ]
[ "nonn" ]
11
1
1
[ "A001147", "A064224", "A100934", "A257836", "A343459", "A360662" ]
null
Ilya Gutkovskiy, Feb 15 2023
2023-03-14T09:28:12
oeisdata/seq/A360/A360662.seq
b0d13006f0326761c4bbc236f953b108
A360663
a(n) is the least integer m >= 3 such that n is a centered m-gonal number.
[ "3", "4", "5", "6", "7", "8", "3", "10", "11", "4", "13", "14", "5", "16", "17", "3", "19", "20", "7", "22", "23", "4", "25", "26", "9", "28", "29", "3", "31", "32", "11", "34", "35", "6", "37", "38", "13", "4", "41", "7", "43", "44", "3", "46", "47", "8", "49", "5", "17", "52", "53", "9", "55", "56", "19", "58", "59", "4", "61", "62", "3", "64", "65", "11", "67", "68", "23", "7", "71", "12", "73", "74", "5", "76", "77", "13", "79" ]
[ "nonn" ]
12
4
1
[ "A101321", "A176774", "A333914", "A360663" ]
null
Ilya Gutkovskiy, Feb 15 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360663.seq
65162a79f774236b85812367e95054bd
A360664
Number of inequivalent n X n matrices using exactly n different symbols, where equivalence means permutations of rows or columns or the symbol set.
[ "1", "1", "4", "121", "316622", "170309112972", "27417944542834007012", "1999576637456562016308833727820", "95614444589289128555388037722252407519896044", "4112190260012069813083100063825969898935642267505877920574871" ]
[ "nonn" ]
8
0
3
[ "A242106", "A360664" ]
null
Alois P. Heinz, Feb 15 2023
2023-02-15T20:53:30
oeisdata/seq/A360/A360664.seq
978aad31053cd321468b1865ecb18363
A360665
Square array T(n, k) = k*((2*n-1)*k+1)/2 read by rising antidiagonals.
[ "0", "0", "0", "0", "1", "-1", "0", "2", "3", "-3", "0", "3", "7", "6", "-6", "0", "4", "11", "15", "10", "-10", "0", "5", "15", "24", "26", "15", "-15", "0", "6", "19", "33", "42", "40", "21", "-21", "0", "7", "23", "42", "58", "65", "57", "28", "-28", "0", "8", "27", "51", "74", "90", "93", "77", "36", "-36", "0", "9", "31", "60", "90", "115", "129", "126", "100", "45", "-45" ]
[ "sign", "tabl", "easy" ]
38
0
8
[ "A000217", "A000290", "A005449", "A005475", "A022265", "A022267", "A022269", "A034827", "A059270", "A081436", "A101986", "A161680", "A162254", "A179297", "A360665", "A360962", "A361226" ]
null
Paul Curtz, Mar 17 2023
2023-04-20T06:41:51
oeisdata/seq/A360/A360665.seq
479d8c89a94d7e7a1fb5b5d10fb46f94
A360666
Semiprimes k such that k+4, k+6, k+9, k+10 and k+14 are also semiprimes.
[ "2977", "5357", "10537", "15697", "15829", "21949", "22417", "23257", "30017", "33509", "33949", "37909", "38509", "46033", "51073", "52333", "58813", "59317", "63937", "68617", "68797", "78409", "84877", "85273", "92513", "94177", "97229", "98233", "100873", "114977", "115697", "118177", "124229", "131977", "137257", "145217", "148637", "153973", "154549", "156193", "159253" ]
[ "nonn" ]
7
1
1
[ "A001358", "A360666" ]
null
Zak Seidov and Robert Israel, Feb 15 2023
2023-02-16T10:11:00
oeisdata/seq/A360/A360666.seq
e1a79e4461a38e525077269790593198
A360667
Triangle read by rows: T(n,m)=4^(n-1)*C(n,m)*C(3*n/2-2,n-1)/n, for 0 <= m <= n, with T(0,0)=1.
[ "1", "1", "1", "2", "4", "2", "10", "30", "30", "10", "64", "256", "384", "256", "64", "462", "2310", "4620", "4620", "2310", "462", "3584", "21504", "53760", "71680", "53760", "21504", "3584", "29172", "204204", "612612", "1021020", "1021020", "612612", "204204", "29172", "245760", "1966080", "6881280", "13762560", "17203200", "13762560", "6881280", "1966080", "245760" ]
[ "nonn", "tabl" ]
12
0
4
[ "A078531", "A360667" ]
null
Vladimir Kruchinin, Feb 16 2023
2023-02-16T11:59:04
oeisdata/seq/A360/A360667.seq
86266460639ddee08b6c38ef008eb565
A360668
Numbers > 1 whose greatest prime index is not divisible by their number of prime factors (bigomega).
[ "4", "8", "10", "12", "15", "16", "18", "22", "24", "25", "27", "28", "32", "33", "34", "36", "40", "42", "44", "46", "48", "51", "54", "55", "60", "62", "63", "64", "66", "68", "69", "70", "72", "76", "77", "80", "81", "82", "85", "88", "90", "93", "94", "96", "98", "99", "100", "102", "104", "105", "108", "110", "112", "114", "115", "116", "118", "119", "120", "121", "123", "124" ]
[ "nonn" ]
9
1
1
[ "A001222", "A008284", "A056239", "A058398", "A067340", "A072978", "A078175", "A112798", "A139710", "A168659", "A200727", "A307683", "A316413", "A326567", "A326568", "A327482", "A334201", "A340610", "A348551", "A359912", "A360551", "A360554", "A360556", "A360557", "A360614", "A360615", "A360668", "A360669", "A360691" ]
null
Gus Wiseman, Feb 17 2023
2023-02-18T20:49:42
oeisdata/seq/A360/A360668.seq
f8a2d48254f1c895913db497189b7739
A360669
Nonprime numbers > 1 for which the prime indices have the same mean as their first differences.
[ "10", "39", "68", "115", "138", "259", "310", "328", "387", "517", "574", "636", "793", "795", "1034", "1168", "1206", "1241", "1281", "1340", "1534", "1691", "1825", "2212", "2278", "2328", "2343", "2369", "2370", "2727", "2774", "2905", "3081", "3277", "3818", "3924", "4064", "4074", "4247", "4268", "4360", "4539", "4850", "4905", "5243", "5335" ]
[ "nonn" ]
5
1
1
[ "A001222", "A008284", "A056239", "A058398", "A088529", "A088530", "A112798", "A124010", "A301987", "A316413", "A326567", "A326568", "A327482", "A334201", "A340610", "A344415", "A348551", "A359904", "A360008", "A360068", "A360614", "A360615", "A360669", "A360670", "A360681" ]
null
Gus Wiseman, Feb 18 2023
2023-02-19T18:02:39
oeisdata/seq/A360/A360669.seq
738d7630374d2de5cd47bac789f15e36
A360670
Number of integer partitions of n whose parts have the same mean as their negated first differences.
[ "1", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "2", "0", "0", "1", "2", "0", "2", "0", "2", "2", "0", "0", "5", "1", "0", "3", "3", "0", "4", "0", "5", "3", "0", "2", "10", "0", "0", "4", "10", "0", "5", "0", "7", "9", "0", "0", "17", "1", "6", "5", "10", "0", "9", "8", "14", "6", "0", "0", "34", "0", "0", "9", "18", "13", "13", "0", "17", "7", "19", "0", "40", "0", "0", "28" ]
[ "nonn" ]
7
0
13
[ "A000009", "A000041", "A008284", "A058398", "A060016", "A067538", "A102627", "A116608", "A240219", "A316313", "A316413", "A326567", "A326568", "A327482", "A340610", "A360068", "A360614", "A360615", "A360669", "A360670" ]
null
Gus Wiseman, Feb 18 2023
2023-02-19T20:52:02
oeisdata/seq/A360/A360670.seq
d58a5b5fb0dea62876e4289c23ca3f51
A360671
Number of multisets whose right half (inclusive) sums to n.
[ "1", "2", "5", "8", "16", "21", "42", "51", "90", "121", "185", "235", "386", "465", "679", "908", "1261", "1580", "2238", "2770", "3827", "4831", "6314", "7910", "10619", "13074", "16813", "21049", "26934", "33072", "42445", "51679", "65264", "79902", "99309", "121548", "151325", "182697", "224873", "272625", "334536", "401999", "491560", "588723" ]
[ "nonn" ]
9
0
2
[ "A000041", "A347044", "A360671", "A360672", "A360673", "A360675", "A360679", "A360954", "A360955", "A360956", "A361200", "A361201" ]
null
Gus Wiseman, Mar 09 2023
2023-03-11T15:07:46
oeisdata/seq/A360/A360671.seq
4e7725008275defc78089ae701c87415
A360672
Triangle read by rows where T(n,k) is the number of integer partitions of n whose left half (exclusive) sums to k, where k ranges from 0 to n.
[ "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "0", "3", "1", "0", "1", "0", "2", "3", "1", "0", "1", "0", "1", "4", "4", "1", "0", "1", "0", "0", "3", "6", "4", "1", "0", "1", "0", "0", "1", "7", "7", "5", "1", "0", "1", "0", "0", "1", "4", "8", "10", "5", "1", "0", "1", "0", "0", "0", "3", "6", "14", "11", "6", "1", "0", "1", "0", "0", "0", "1", "5", "12", "16", "14", "6", "1", "0" ]
[ "nonn", "tabl" ]
13
0
13
[ "A000041", "A008284", "A027193", "A237363", "A307683", "A325347", "A347043", "A347044", "A359893", "A359901", "A360005", "A360071", "A360254", "A360616", "A360671", "A360672", "A360673", "A360674", "A360675", "A360676", "A360677", "A360678", "A360679", "A360682", "A360686", "A360953", "A361200", "A361201" ]
null
Gus Wiseman, Feb 27 2023
2023-03-11T23:06:27
oeisdata/seq/A360/A360672.seq
a8e0f581e86b6ff429ed395bb4073dcd
A360673
Number of multisets of positive integers whose right half (exclusive) sums to n.
[ "1", "2", "7", "13", "27", "37", "73", "89", "156", "205", "315", "387", "644", "749", "1104", "1442", "2015", "2453", "3529", "4239", "5926", "7360", "9624", "11842", "16115", "19445", "25084", "31137", "39911", "48374", "62559", "75135", "95263", "115763", "143749", "174874", "218614", "261419", "321991", "388712", "477439", "569968", "698493" ]
[ "nonn" ]
15
0
2
[ "A000041", "A347043", "A347044", "A359893", "A359901", "A360616", "A360617", "A360671", "A360672", "A360673", "A360674", "A360675", "A360676", "A360677", "A360678", "A360679", "A360953", "A360954", "A360955", "A360956", "A361200", "A361201" ]
null
Gus Wiseman, Mar 04 2023
2023-03-11T15:07:42
oeisdata/seq/A360/A360673.seq
39a1951a5b64af13333c276cddee8aac
A360674
Number of integer partitions of 2n whose left half (exclusive) and right half (inclusive) both sum to n.
[ "1", "1", "3", "4", "7", "6", "12", "9", "16", "15", "21", "16", "34", "22", "33", "36", "47", "36", "62", "44", "75", "68", "78", "68", "120", "93", "113", "117", "151", "122", "195", "148", "209", "197", "220", "226", "315", "249", "304", "309", "402", "332", "463", "387", "496", "515", "539", "514", "712", "609", "738", "723", "845", "774", "983", "914", "1111" ]
[ "nonn" ]
13
0
3
[ "A000005", "A000041", "A008284", "A237363", "A347043", "A347044", "A359893", "A359901", "A360254", "A360671", "A360672", "A360673", "A360674", "A360675", "A360676", "A360677", "A360678", "A360679", "A360682", "A360953", "A361200", "A361201" ]
null
Gus Wiseman, Mar 04 2023
2023-03-09T20:03:32
oeisdata/seq/A360/A360674.seq
6ae01f7cc8abb96d5a7c5d71d8c6e07b
A360675
Triangle read by rows where T(n,k) is the number of integer partitions of n whose right half (exclusive) sums to k, where k ranges from 0 to n.
[ "1", "1", "0", "1", "1", "0", "1", "2", "0", "0", "1", "2", "2", "0", "0", "1", "3", "3", "0", "0", "0", "1", "3", "5", "2", "0", "0", "0", "1", "4", "6", "4", "0", "0", "0", "0", "1", "4", "9", "5", "3", "0", "0", "0", "0", "1", "5", "10", "10", "4", "0", "0", "0", "0", "0", "1", "5", "13", "12", "9", "2", "0", "0", "0", "0", "0", "1", "6", "15", "18", "11", "5", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "tabl" ]
12
0
8
[ "A000005", "A000041", "A008284", "A027193", "A237363", "A307683", "A325347", "A347043", "A347044", "A359893", "A359901", "A360005", "A360071", "A360254", "A360616", "A360671", "A360672", "A360673", "A360674", "A360675", "A360676", "A360677", "A360678", "A360679", "A360953", "A361200", "A361201" ]
null
Gus Wiseman, Feb 27 2023
2023-03-11T23:06:22
oeisdata/seq/A360/A360675.seq
da897af364f0e5491334c263d193b700
A360676
Sum of the left half (exclusive) of the prime indices of n.
[ "0", "0", "0", "1", "0", "1", "0", "1", "2", "1", "0", "1", "0", "1", "2", "2", "0", "1", "0", "1", "2", "1", "0", "2", "3", "1", "2", "1", "0", "1", "0", "2", "2", "1", "3", "2", "0", "1", "2", "2", "0", "1", "0", "1", "2", "1", "0", "2", "4", "1", "2", "1", "0", "3", "3", "2", "2", "1", "0", "2", "0", "1", "2", "3", "3", "1", "0", "1", "2", "1", "0", "2", "0", "1", "2", "1", "4", "1", "0", "2", "4", "1", "0", "2", "3", "1", "2" ]
[ "nonn" ]
14
1
9
[ "A000040", "A001222", "A001248", "A026424", "A056239", "A112798", "A280076", "A347043", "A347044", "A359912", "A360005", "A360006", "A360457", "A360616", "A360617", "A360671", "A360672", "A360673", "A360674", "A360675", "A360676", "A360677", "A360678", "A360679", "A361200", "A361201" ]
null
Gus Wiseman, Mar 04 2023
2025-02-03T02:23:35
oeisdata/seq/A360/A360676.seq
4f0dde6f66bbfe4b3daf354fa8567e94
A360677
Sum of the right half (exclusive) of the prime indices of n.
[ "0", "0", "0", "1", "0", "2", "0", "1", "2", "3", "0", "2", "0", "4", "3", "2", "0", "2", "0", "3", "4", "5", "0", "3", "3", "6", "2", "4", "0", "3", "0", "2", "5", "7", "4", "4", "0", "8", "6", "4", "0", "4", "0", "5", "3", "9", "0", "3", "4", "3", "7", "6", "0", "4", "5", "5", "8", "10", "0", "5", "0", "11", "4", "3", "6", "5", "0", "7", "9", "4", "0", "4", "0", "12", "3", "8", "5", "6", "0", "4", "4", "13", "0", "6", "7" ]
[ "nonn" ]
8
1
6
[ "A000040", "A001222", "A001248", "A004171", "A026424", "A056239", "A100484", "A112798", "A347043", "A347044", "A359908", "A359912", "A360005", "A360006", "A360457", "A360616", "A360617", "A360671", "A360672", "A360673", "A360675", "A360676", "A360677", "A360678", "A360679", "A361200", "A361201" ]
null
Gus Wiseman, Mar 05 2023
2023-03-07T22:10:32
oeisdata/seq/A360/A360677.seq
725650d605f0e86268de8992cc344848
A360678
Sum of the left half (inclusive) of the prime indices of n.
[ "0", "1", "2", "1", "3", "1", "4", "2", "2", "1", "5", "2", "6", "1", "2", "2", "7", "3", "8", "2", "2", "1", "9", "2", "3", "1", "4", "2", "10", "3", "11", "3", "2", "1", "3", "2", "12", "1", "2", "2", "13", "3", "14", "2", "4", "1", "15", "3", "4", "4", "2", "2", "16", "3", "3", "2", "2", "1", "17", "2", "18", "1", "4", "3", "3", "3", "19", "2", "2", "4", "20", "3", "21", "1", "5", "2", "4", "3", "22", "3", "4", "1" ]
[ "nonn" ]
6
1
3
[ "A001222", "A001248", "A001747", "A026424", "A056239", "A112798", "A280076", "A347043", "A347044", "A359912", "A360005", "A360006", "A360457", "A360616", "A360617", "A360671", "A360672", "A360673", "A360675", "A360676", "A360677", "A360678", "A360679", "A361200", "A361201" ]
null
Gus Wiseman, Mar 05 2023
2023-03-07T22:10:21
oeisdata/seq/A360/A360678.seq
e8c586c81fe16306285769fd3c0c7d4c
A360679
Sum of the right half (inclusive) of the prime indices of n.
[ "0", "1", "2", "1", "3", "2", "4", "2", "2", "3", "5", "3", "6", "4", "3", "2", "7", "4", "8", "4", "4", "5", "9", "3", "3", "6", "4", "5", "10", "5", "11", "3", "5", "7", "4", "4", "12", "8", "6", "4", "13", "6", "14", "6", "5", "9", "15", "4", "4", "6", "7", "7", "16", "4", "5", "5", "8", "10", "17", "5", "18", "11", "6", "3", "6", "7", "19", "8", "9", "7", "20", "5", "21", "12", "6", "9", "5", "8", "22", "5", "4" ]
[ "nonn" ]
6
1
3
[ "A001222", "A001248", "A026424", "A056239", "A112798", "A347043", "A347044", "A359912", "A360005", "A360006", "A360007", "A360457", "A360616", "A360617", "A360671", "A360672", "A360673", "A360675", "A360676", "A360677", "A360678", "A360679", "A361200", "A361201" ]
null
Gus Wiseman, Mar 05 2023
2023-03-07T22:10:16
oeisdata/seq/A360/A360679.seq
96b66d6deb455c361bfd13187fb1672d
A360680
Numbers for which the prime signature has the same mean as the first differences of 0-prepended prime indices.
[ "1", "2", "6", "30", "49", "152", "210", "513", "1444", "1776", "1952", "2310", "2375", "2664", "2760", "2960", "3249", "3864", "3996", "4140", "4144", "5796", "5994", "6072", "6210", "6440", "6512", "6517", "6900", "7176", "7400", "7696", "8694", "9025", "9108", "9384", "10064", "10120", "10350", "10488", "10764", "11248", "11960", "12167" ]
[ "nonn" ]
6
1
2
[ "A001222", "A056239", "A088529", "A088530", "A112798", "A124010", "A316413", "A326567", "A326568", "A326619", "A326620", "A340610", "A348551", "A359903", "A359904", "A359905", "A360008", "A360068", "A360460", "A360555", "A360556", "A360614", "A360615", "A360680", "A360681" ]
null
Gus Wiseman, Feb 19 2023
2023-02-20T07:54:33
oeisdata/seq/A360/A360680.seq
ff875fa81919e47bc8eb260e7f21ab31
A360681
Numbers for which the prime signature has the same median as the first differences of 0-prepended prime indices.
[ "1", "2", "6", "30", "42", "49", "60", "66", "70", "78", "84", "90", "102", "105", "114", "120", "126", "132", "138", "140", "150", "154", "156", "168", "174", "186", "198", "204", "210", "222", "228", "234", "246", "258", "264", "270", "276", "280", "282", "286", "294", "306", "308", "312", "315", "318", "330", "342", "348", "350", "354", "366", "372", "378", "385" ]
[ "nonn" ]
5
1
2
[ "A000975", "A001222", "A026424", "A056239", "A063655", "A072978", "A088529", "A088530", "A100367", "A112798", "A118914", "A124010", "A139710", "A139711", "A307683", "A316413", "A325347", "A326567", "A326568", "A340610", "A359893", "A359901", "A359902", "A359904", "A359907", "A359908", "A359912", "A359913", "A360005", "A360006", "A360248", "A360453", "A360457", "A360458", "A360459", "A360460", "A360550", "A360551", "A360552", "A360553", "A360554", "A360555", "A360556", "A360557", "A360558", "A360680", "A360681", "A360687", "A360688" ]
null
Gus Wiseman, Feb 19 2023
2023-02-19T20:51:57
oeisdata/seq/A360/A360681.seq
f9b50497478fc8cc0b183710db67f21c
A360682
Number of integer partitions of n of length > 2 whose second differences have median 0.
[ "0", "0", "0", "1", "1", "1", "5", "4", "10", "13", "18", "23", "44", "44", "72", "98", "132", "162", "241", "277", "394", "497", "643", "800", "1076", "1287", "1660", "2078", "2604", "3192", "4065", "4892", "6113", "7490", "9166", "11110", "13717", "16429", "20033", "24201", "29143", "34945", "42251", "50219", "60253", "71852", "85503", "101501", "120899" ]
[ "nonn" ]
6
0
7
[ "A000009", "A000041", "A000975", "A008284", "A008619", "A027193", "A067538", "A114638", "A237363", "A307683", "A325347", "A359893", "A359901", "A359902", "A359907", "A359908", "A360005", "A360245", "A360254", "A360682", "A360683", "A360687", "A360688" ]
null
Gus Wiseman, Feb 19 2023
2023-02-20T21:49:20
oeisdata/seq/A360/A360682.seq
e37669c14231231156fe55a1658598d0
A360683
Number of integer partitions of n whose second differences sum to 0, meaning either there is only one part, or the first two parts have the same difference as the last two parts.
[ "1", "1", "2", "3", "4", "4", "8", "6", "11", "12", "17", "14", "32", "23", "40", "44", "64", "59", "104", "93", "149", "157", "218", "227", "342", "349", "481", "538", "713", "777", "1052", "1145", "1494", "1692", "2130", "2416", "3064", "3449", "4286", "4918", "6028", "6882", "8424", "9620", "11634", "13396", "16022", "18416", "22019", "25248", "29954" ]
[ "nonn" ]
6
0
3
[ "A000009", "A000041", "A008284", "A008619", "A067538", "A102627", "A114638", "A240219", "A316413", "A325347", "A348551", "A360068", "A360682", "A360683" ]
null
Gus Wiseman, Feb 19 2023
2023-02-20T21:49:25
oeisdata/seq/A360/A360683.seq
ba9112ab31e055661750176d3b35c195
A360684
Expansion of Sum_{k>=0} (x * (1 + k^2 * x))^k.
[ "1", "1", "2", "9", "44", "308", "2391", "22851", "241570", "2937179", "39192998", "579482352", "9328260061", "162563246381", "3062996934322", "61499850730949", "1327236820161040", "30176760155713420", "733829463528115523", "18639130961053854975", "504241689606231891890" ]
[ "nonn" ]
14
0
3
[ "A355471", "A360592", "A360647", "A360684" ]
null
Seiichi Manyama, Feb 16 2023
2023-02-16T09:33:00
oeisdata/seq/A360/A360684.seq
18a35e28f201a38ca038e7b61f443a91
A360685
Number of maximum independent vertex sets in the n-halved cube graph Q_n/2.
[ "1", "2", "4", "4", "40", "120", "240", "240", "11612160" ]
[ "nonn", "more", "hard" ]
14
1
2
[ "A290606", "A360685" ]
null
Eric W. Weisstein, Feb 16 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360685.seq
fb6ee6c87517d04ef96845f50222547f
A360686
Number of integer partitions of n whose distinct parts have integer median.
[ "1", "2", "2", "4", "3", "8", "7", "16", "17", "31", "35", "60", "67", "99", "121", "170", "200", "270", "328", "436", "522", "674", "828", "1061", "1292", "1626", "1983", "2507", "3035", "3772", "4582", "5661", "6801", "8358", "10059", "12231", "14627", "17702", "21069", "25423", "30147", "36100", "42725", "50936", "60081", "71388", "84007", "99408" ]
[ "nonn" ]
9
1
2
[ "A000009", "A000041", "A000975", "A026424", "A027193", "A067538", "A067659", "A102627", "A116608", "A240219", "A307683", "A316413", "A325347", "A326621", "A359893", "A359901", "A359902", "A359906", "A359907", "A359908", "A360005", "A360071", "A360241", "A360244", "A360245", "A360550", "A360551", "A360556", "A360686", "A360687", "A360688", "A360689" ]
null
Gus Wiseman, Feb 20 2023
2023-02-22T08:08:12
oeisdata/seq/A360/A360686.seq
af2093f8200d14e220f9c962d72ef7e0
A360687
Number of integer partitions of n whose multiplicities have integer median.
[ "1", "2", "3", "4", "5", "9", "10", "16", "22", "34", "42", "65", "80", "115", "145", "195", "240", "324", "396", "519", "635", "814", "994", "1270", "1549", "1952", "2378", "2997", "3623", "4521", "5466", "6764", "8139", "10008", "12023", "14673", "17534", "21273", "25336", "30593", "36302", "43575", "51555", "61570", "72653", "86382", "101676" ]
[ "nonn" ]
10
1
2
[ "A000975", "A008284", "A058398", "A067340", "A088529", "A088530", "A090794", "A118914", "A124010", "A307683", "A325347", "A327482", "A329976", "A359893", "A359901", "A359902", "A359907", "A359908", "A360068", "A360069", "A360460", "A360550", "A360553", "A360554", "A360556", "A360687", "A360688", "A360690" ]
null
Gus Wiseman, Feb 20 2023
2023-02-27T07:46:04
oeisdata/seq/A360/A360687.seq
e714d13eadaf3ab4d50dda0e4bd7f722
A360688
Number of integer partitions of n with integer median of 0-appended first differences.
[ "1", "1", "3", "4", "5", "7", "12", "18", "25", "32", "46", "62", "79", "109", "142", "189", "240", "322", "405", "522", "671", "853", "1053", "1345", "1653", "2081", "2551", "3174", "3878", "4826", "5851", "7219", "8747", "10712", "12936", "15719", "18876", "22872", "27365", "32926", "39253", "47070", "55857", "66676", "79029", "93864", "110832" ]
[ "nonn" ]
6
1
3
[ "A000009", "A000041", "A000975", "A008284", "A027193", "A237363", "A240219", "A325347", "A359893", "A359901", "A359902", "A359907", "A359908", "A360254", "A360455", "A360555", "A360556", "A360557", "A360558", "A360688" ]
null
Gus Wiseman, Feb 20 2023
2023-02-22T08:07:58
oeisdata/seq/A360/A360688.seq
391a51a10e91e6ba67aceab15b3129e9
A360689
Number of integer partitions of n whose distinct parts have non-integer median.
[ "0", "0", "1", "1", "4", "3", "8", "6", "13", "11", "21", "17", "34", "36", "55", "61", "97", "115", "162", "191", "270", "328", "427", "514", "666", "810", "1027", "1211", "1530", "1832", "2260", "2688", "3342", "3952", "4824", "5746", "7010", "8313", "10116", "11915", "14436", "17074", "20536", "24239", "29053", "34170", "40747", "47865", "56830", "66621" ]
[ "nonn" ]
6
1
5
[ "A000009", "A000041", "A000975", "A027193", "A090794", "A116608", "A240219", "A307683", "A325347", "A349156", "A359893", "A359901", "A359902", "A359907", "A359912", "A360005", "A360071", "A360241", "A360244", "A360245", "A360457", "A360550", "A360551", "A360554", "A360686", "A360689", "A360690" ]
null
Gus Wiseman, Feb 22 2023
2023-02-24T21:46:55
oeisdata/seq/A360/A360689.seq
0072f33f60bb685740818771fa95916b
A360690
Number of integer partitions of n with non-integer median of multiplicities.
[ "0", "0", "0", "1", "2", "2", "5", "6", "8", "8", "14", "12", "21", "20", "31", "36", "57", "61", "94", "108", "157", "188", "261", "305", "409", "484", "632", "721", "942", "1083", "1376", "1585", "2004", "2302", "2860", "3304", "4103", "4742", "5849", "6745", "8281", "9599", "11706", "13605", "16481", "19176", "23078", "26838", "32145", "37387", "44465" ]
[ "nonn" ]
6
1
5
[ "A000041", "A000975", "A008284", "A058398", "A067340", "A088529", "A088530", "A090794", "A118914", "A124010", "A307683", "A325347", "A327482", "A329976", "A359893", "A359901", "A359902", "A359907", "A359908", "A360068", "A360069", "A360460", "A360550", "A360553", "A360554", "A360556", "A360687", "A360688", "A360690" ]
null
Gus Wiseman, Feb 22 2023
2023-02-24T21:46:46
oeisdata/seq/A360/A360690.seq
6bb4d3a7097ffbbd1ea19aac68449177
A360691
Number of integer partitions of n with non-integer median of 0-prepended first differences.
[ "0", "1", "0", "1", "2", "4", "3", "4", "5", "10", "10", "15", "22", "26", "34", "42", "57", "63", "85", "105", "121", "149", "202", "230", "305", "355", "459", "544", "687", "778", "991", "1130", "1396", "1598", "1947", "2258", "2761", "3143", "3820", "4412", "5330", "6104", "7404", "8499", "10105", "11694", "13922", "15917", "18904", "21646", "25462", "29213" ]
[ "nonn" ]
5
1
5
[ "A000009", "A000041", "A000975", "A008284", "A027193", "A237363", "A240219", "A307683", "A325347", "A359893", "A359901", "A359902", "A359907", "A359908", "A360254", "A360455", "A360555", "A360556", "A360557", "A360558", "A360688", "A360691" ]
null
Gus Wiseman, Feb 22 2023
2023-02-24T21:46:41
oeisdata/seq/A360/A360691.seq
d810a6b7c53c05576f1987c8aae5585e
A360692
a(0) = 0. Thereafter a(n+1) = a(a(n)) if a(n) has not occurred previously, otherwise a(n+1) = n - 1 - a(n-1).
[ "0", "0", "0", "1", "0", "2", "0", "3", "1", "4", "0", "5", "2", "6", "0", "7", "3", "8", "1", "9", "4", "10", "0", "11", "5", "12", "2", "13", "6", "14", "0", "15", "7", "16", "3", "17", "8", "18", "1", "19", "9", "20", "4", "21", "10", "22", "0", "23", "11", "24", "5", "25", "12", "26", "2", "27", "13", "28", "6", "29", "14", "30", "0", "31", "15", "32", "7", "33", "16", "34", "3", "35", "17", "36", "8" ]
[ "nonn" ]
29
0
6
[ "A000225", "A027383", "A051633", "A101279", "A176449", "A176488", "A360692" ]
null
David James Sycamore, Feb 16 2023
2025-03-25T02:27:31
oeisdata/seq/A360/A360692.seq
9243130ea3b6ee7ffc7286aba51df214
A360693
Number T(n,k) of sets of n words of length n over binary alphabet where the first letter occurs k times; triangle T(n,k), n>=0, n-signum(n)<=k<=n*(n-1)+signum(n), read by rows.
[ "1", "1", "1", "2", "2", "2", "3", "10", "15", "15", "10", "3", "4", "37", "108", "228", "336", "394", "336", "228", "108", "37", "4", "5", "101", "600", "2150", "5645", "11680", "19752", "27820", "32935", "32935", "27820", "19752", "11680", "5645", "2150", "600", "101", "5", "6", "226", "2490", "14745", "61770", "200529", "535674", "1211485", "2368200" ]
[ "nonn", "tabf" ]
36
0
4
[ "A000027", "A000290", "A014070", "A057427", "A154323", "A220886", "A360693", "A360695", "A360702" ]
null
Alois P. Heinz, Feb 16 2023
2023-05-26T03:49:06
oeisdata/seq/A360/A360693.seq
0360fff8164517a1154cb45947f82cc7
A360694
Numbers whose divisors can be partitioned into two disjoint sets where the sum of both sets is prime.
[ "4", "6", "8", "10", "12", "14", "15", "16", "18", "20", "21", "22", "24", "26", "27", "28", "30", "32", "33", "34", "35", "36", "38", "39", "40", "42", "44", "45", "48", "52", "54", "55", "56", "57", "58", "60", "63", "65", "66", "68", "69", "70", "72", "75", "76", "77", "78", "80", "82", "84", "85", "86", "88", "90", "92", "93", "94", "95", "96", "99", "102", "104", "105", "106", "108", "110", "111", "112", "114", "115" ]
[ "nonn" ]
74
1
1
[ "A000040", "A000203", "A000396", "A028982", "A083207", "A360694" ]
null
Zoltan Galantai, Feb 17 2023
2023-03-21T18:07:47
oeisdata/seq/A360/A360694.seq
045c82a250d284cb289b331f8ecdb9a3
A360695
Total number of sets of k words of length k over binary alphabet with exactly n occurrences of the first letter in the set, summed over all k >= 0.
[ "2", "3", "5", "16", "57", "230", "1071", "5429", "29810", "175718", "1101090", "7294593", "50829712", "370975443", "2826022446", "22403032310", "184339146428", "1570830751662", "13835026646912", "125719891784479", "1176838995406439", "11331919317891519", "112100167281082176", "1137938904082103310" ]
[ "nonn" ]
25
0
1
[ "A360693", "A360695" ]
null
Alois P. Heinz, Feb 16 2023
2023-12-13T14:43:50
oeisdata/seq/A360/A360695.seq
d9804452af5d61cf48fabef4ecd2187a
A360696
Expansion of Sum_{k>=0} (x * (1 + k^k * x))^k.
[ "1", "1", "2", "9", "98", "3212", "428525", "165045051", "342128248388", "2522279110319003", "90930729844450829580", "17690430223837969605522024", "13516362920784209950583739768297", "79459280482613898608830749440741093093" ]
[ "nonn" ]
10
0
3
[ "A000045", "A355463", "A360592", "A360684", "A360696" ]
null
Seiichi Manyama, Feb 16 2023
2023-02-16T12:21:59
oeisdata/seq/A360/A360696.seq
07bd573dafdbf730f5077370760080d1
A360697
The sum of the squares of the digits of n, repeated until reaching a single-digit number.
[ "0", "1", "4", "9", "4", "4", "4", "1", "4", "4", "1", "2", "5", "1", "4", "4", "4", "4", "4", "1", "4", "5", "8", "1", "4", "4", "4", "4", "1", "4", "9", "1", "1", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "1", "4", "4", "4", "4", "1", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "1", "4", "1", "4", "4", "4", "4", "4", "4", "4", "2", "1", "4", "4", "1", "4", "4", "4", "1", "2", "4", "4", "4", "1", "4", "4", "1", "4", "4", "1", "4", "4", "1" ]
[ "nonn", "base" ]
31
0
3
[ "A003132", "A007770", "A099645", "A360697" ]
null
Will Nicholes, Feb 16 2023
2023-03-02T22:59:52
oeisdata/seq/A360/A360697.seq
d82d563cac20a380ee3e1f5a00641434
A360698
Smallest number that is a sum of 2*k+1 consecutive prime numbers for each k in {1, 2, ..., n}.
[ "10", "83", "311", "400861", "656303169", "460787266801", "108315769373443" ]
[ "nonn", "more" ]
9
1
1
[ "A222564", "A222592", "A288340", "A360698" ]
null
Max Alekseyev, Feb 16 2023
2023-02-17T22:24:20
oeisdata/seq/A360/A360698.seq
11665fd926701863c334d100e3e60f28
A360699
G.f.: Sum_{k>=0} (1 + k*x)^k * x^(2*k).
[ "1", "0", "1", "1", "1", "4", "5", "9", "28", "43", "97", "281", "507", "1286", "3666", "7494", "20470", "58725", "132484", "381700", "1113180", "2719887", "8171219", "24337511", "63524916", "197606643", "602261524", "1662206380", "5328738685", "16628469912", "48148703533", "158544768073", "506473892417", "1529218062752", "5159071807165" ]
[ "nonn" ]
13
0
6
[ "A360479", "A360592", "A360699", "A360707" ]
null
Vaclav Kotesovec, Feb 16 2023
2023-02-20T03:16:36
oeisdata/seq/A360/A360699.seq
dca0d5e33422bee9ffc0fc4e193a7191
A360700
Decimal expansion of arcsec(Pi).
[ "1", "2", "4", "6", "8", "5", "0", "2", "1", "9", "8", "6", "2", "9", "1", "5", "8", "9", "9", "2", "5", "0", "3", "6", "8", "8", "6", "1", "0", "1", "0", "9", "7", "7", "6", "0", "6", "4", "2", "5", "8", "2", "8", "5", "7", "4", "2", "1", "5", "4", "3", "1", "5", "8", "4", "9", "5", "0", "4", "1", "0", "9", "1", "7", "8", "9", "4", "3", "2", "3", "9", "7", "3", "9", "6", "2", "2", "0", "1", "6", "0", "9", "1", "2", "1", "6", "7", "9", "3", "5", "3", "7", "3", "2", "1", "0", "4", "1", "9", "0", "2", "0", "4", "8", "0" ]
[ "cons", "nonn" ]
15
1
2
[ "A232272", "A232273", "A360700", "A360701" ]
null
Wolfe Padawer, Feb 16 2023
2023-03-13T09:15:29
oeisdata/seq/A360/A360700.seq
5011fcef33103e01cff7ab1d9073959d