Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
seq_id
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573
sequence
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348
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1
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score
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int64
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int64
5
5
cross_references
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-25 01:21:50
filename
stringlengths
29
29
hash
stringlengths
32
32
A001401
Number of partitions of n into at most 5 parts.
[ "1", "1", "2", "3", "5", "7", "10", "13", "18", "23", "30", "37", "47", "57", "70", "84", "101", "119", "141", "164", "192", "221", "255", "291", "333", "377", "427", "480", "540", "603", "674", "748", "831", "918", "1014", "1115", "1226", "1342", "1469", "1602", "1747", "1898", "2062", "2233", "2418", "2611", "2818", "3034", "3266", "3507", "3765", "4033", "4319" ]
[ "nonn", "easy", "nice" ]
108
0
5
[ "A001399", "A001400", "A001401", "A002622", "A008284", "A008619", "A008667", "A008804" ]
[ "M0642", "N0237" ]
N. J. A. Sloane
2024-08-28T00:56:34
oeisdata/seq/A001/A001401.seq
0bc2983e0a82f7fef1cd1b05f045fceb
A001402
Number of partitions of n into at most 6 parts.
[ "1", "1", "2", "3", "5", "7", "11", "14", "20", "26", "35", "44", "58", "71", "90", "110", "136", "163", "199", "235", "282", "331", "391", "454", "532", "612", "709", "811", "931", "1057", "1206", "1360", "1540", "1729", "1945", "2172", "2432", "2702", "3009", "3331", "3692", "4070", "4494", "4935", "5427", "5942", "6510", "7104", "7760", "8442", "9192" ]
[ "nonn", "easy" ]
177
0
5
[ "A001402", "A008284", "A026812", "A037145", "A194197", "A288341" ]
[ "M0662", "N0243" ]
N. J. A. Sloane
2022-09-11T09:35:18
oeisdata/seq/A001/A001402.seq
f74a8924f87bbd36be99a00014b82105
A001403
Number of combinatorial configurations of type (n_3).
[ "0", "0", "0", "0", "0", "0", "1", "1", "3", "10", "31", "229", "2036", "21399", "245342", "3004881", "38904499", "530452205", "7640941062" ]
[ "nonn", "nice", "hard", "more", "changed" ]
59
0
5
[ "A001403", "A023994", "A098702", "A098804", "A098822", "A098841", "A098851", "A098852", "A098854", "A099999", "A100001" ]
null
N. J. A. Sloane, D.Glynn(AT)math.canterbury.ac.nz
2025-04-20T03:33:19
oeisdata/seq/A001/A001403.seq
1af3dc249830b0c8b9c964db8804c16d
A001404
Triangle of values of 2-d recurrence.
[ "1", "1", "1", "2", "2", "1", "4", "5", "2", "1", "9", "11", "5", "2", "1", "20", "25", "12", "5", "2", "1", "45", "57", "27", "12", "5", "2", "1", "102", "129", "62", "28", "12", "5", "2", "1", "231", "293", "141", "64", "28", "12", "5", "2", "1", "524", "665", "321", "146", "65", "28", "12", "5", "2", "1", "1189", "1510", "729", "333", "148", "65", "28", "12", "5", "2", "1", "2699", "3428", "1656" ]
[ "tabl", "nonn", "easy" ]
17
0
5
[ "A001404", "A001410" ]
null
N. J. A. Sloane [ I have temporarily mislaid the name of the person who sent this ]
2013-06-11T16:22:10
oeisdata/seq/A001/A001404.seq
8acf434d1acaba4044bc32b052ac2d48
A001405
a(n) = binomial(n, floor(n/2)).
[ "1", "1", "2", "3", "6", "10", "20", "35", "70", "126", "252", "462", "924", "1716", "3432", "6435", "12870", "24310", "48620", "92378", "184756", "352716", "705432", "1352078", "2704156", "5200300", "10400600", "20058300", "40116600", "77558760", "155117520", "300540195", "601080390", "1166803110" ]
[ "nonn", "easy", "nice", "core", "walk" ]
643
0
5
[ "A000045", "A000712", "A000984", "A001006", "A001405", "A001700", "A005773", "A005817", "A007578", "A007579", "A022916", "A022917", "A028495", "A036256", "A037952", "A049401", "A051920", "A053121", "A061551", "A061854", "A061855", "A063886", "A088855", "A094718", "A097331", "A107373", "A130820", "A132815", "A153585", "A182172", "A239241", "A265848", "A335570", "A340567", "A340568", "A340569" ]
[ "M0769", "N0294" ]
N. J. A. Sloane
2025-03-19T07:17:51
oeisdata/seq/A001/A001405.seq
03463f8edfc9b88f8da8aaf3d963ce46
A001406
High temperature series for partition function for spin-1/2 Ising model on b.c.c. lattice.
[ "1", "0", "12", "148", "2568", "53944", "1283270", "33268932", "918420570" ]
[ "nonn", "more" ]
27
0
5
[ "A001393", "A001406", "A001407" ]
[ "M4871", "N2086" ]
N. J. A. Sloane
2022-02-15T02:26:31
oeisdata/seq/A001/A001406.seq
3b0e11f3babb6b20fe3e3eea28e775ff
A001407
High temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.
[ "1", "0", "0", "8", "33", "168", "962", "5928", "38907", "268056", "1918938", "14169360", "107333498", "830660688", "6546655404", "52410001448" ]
[ "nonn", "more" ]
30
0
5
[ "A001393", "A001406", "A001407", "A002892", "A002918", "A047712" ]
[ "M4511", "N1909" ]
N. J. A. Sloane
2023-01-19T02:07:35
oeisdata/seq/A001/A001407.seq
038ae4c24d21c76edce47f90ced41f3b
A001408
High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice, divided by 3.
[ "1", "11", "188", "2992", "51708", "930436", "17127356", "320726028", "6086177116", "116714440696", "2257460877244", "43974184178012", "861732730297212", "16973299816150504", "335797855252698940", "6669051330542560708", "132899989069230881308", "2656406833061149357920", "53239449964640093020476" ]
[ "nonn", "nice" ]
31
0
5
[ "A001408", "A002916" ]
[ "M4808", "N2055" ]
N. J. A. Sloane
2022-02-15T11:40:19
oeisdata/seq/A001/A001408.seq
1a0b4e611f339d57f2ddafd43bc0fba7
A001409
Number of 2n-step polygons on cubic lattice.
[ "1", "0", "3", "22", "207", "2412", "31754", "452640", "6840774", "108088232", "1768560270", "29764630632", "512705615350", "9005206632672", "160810554015408", "2912940755956084", "53424552150523386" ]
[ "nonn", "walk", "more" ]
27
0
5
[ "A001409", "A001412" ]
[ "M3095", "N1254" ]
N. J. A. Sloane
2019-08-03T17:14:35
oeisdata/seq/A001/A001409.seq
39af190ee8b6c53e10d1bcf857706970
A001410
Sum of rows of triangle defined in A001404.
[ "1", "2", "5", "12", "28", "65", "149", "341", "777", "1769", "4022", "9140", "20763", "47156", "107086", "243162", "552128", "1253640", "2846424", "6462827", "14673824", "33316766", "75645245", "171751292", "389958283", "885393129", "2010268490" ]
[ "nonn", "easy" ]
16
0
5
[ "A001404", "A001410" ]
null
N. J. A. Sloane
2022-02-01T23:56:54
oeisdata/seq/A001/A001410.seq
e779dd30347aff3122ca2eb37a5edcfb
A001411
Number of n-step self-avoiding walks on square lattice.
[ "1", "4", "12", "36", "100", "284", "780", "2172", "5916", "16268", "44100", "120292", "324932", "881500", "2374444", "6416596", "17245332", "46466676", "124658732", "335116620", "897697164", "2408806028", "6444560484", "17266613812", "46146397316", "123481354908", "329712786220", "881317491628" ]
[ "nonn", "walk", "nice" ]
84
0
5
[ "A001411", "A002900" ]
[ "M3448", "N1402" ]
N. J. A. Sloane, Anthony Guttmann
2024-08-05T13:38:20
oeisdata/seq/A001/A001411.seq
150ec269f66196b6795d6a4826b21b94
A001412
Number of n-step self-avoiding walks on cubic lattice.
[ "1", "6", "30", "150", "726", "3534", "16926", "81390", "387966", "1853886", "8809878", "41934150", "198842742", "943974510", "4468911678", "21175146054", "100121875974", "473730252102", "2237723684094", "10576033219614", "49917327838734", "235710090502158", "1111781983442406", "5245988215191414", "24730180885580790", "116618841700433358", "549493796867100942", "2589874864863200574", "12198184788179866902", "57466913094951837030", "270569905525454674614" ]
[ "nonn", "walk", "nice" ]
78
0
5
[ "A001411", "A001412", "A001413", "A002902", "A078717" ]
[ "M4202", "N1754" ]
N. J. A. Sloane
2024-08-05T13:39:08
oeisdata/seq/A001/A001412.seq
a66a836e8e3d4e22647414e4a8914850
A001413
Number of 2n-step polygons on cubic lattice.
[ "0", "24", "264", "3312", "48240", "762096", "12673920", "218904768", "3891176352", "70742410800", "1309643747808", "24609869536800", "468270744898944", "9005391024862848", "174776445357365040", "3419171337633496704" ]
[ "nonn", "walk", "more" ]
34
0
5
[ "A001409", "A001413", "A002896", "A010566" ]
[ "M5154", "N2238" ]
N. J. A. Sloane
2024-02-29T11:28:04
oeisdata/seq/A001/A001413.seq
c26e09e0c5f61b2bb9b59f410db0f0c0
A001414
Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n).
[ "0", "2", "3", "4", "5", "5", "7", "6", "6", "7", "11", "7", "13", "9", "8", "8", "17", "8", "19", "9", "10", "13", "23", "9", "10", "15", "9", "11", "29", "10", "31", "10", "14", "19", "12", "10", "37", "21", "16", "11", "41", "12", "43", "15", "11", "25", "47", "11", "14", "12", "20", "17", "53", "11", "16", "13", "22", "31", "59", "12", "61", "33", "13", "12", "18", "16", "67", "21", "26", "14", "71", "12", "73", "39", "13", "23", "18", "18" ]
[ "nonn", "easy", "nice" ]
199
0
5
[ "A000607", "A000792", "A001222", "A001414", "A002217", "A008472", "A036288", "A036349", "A046343", "A056239", "A056240", "A059975", "A064097", "A067666", "A104244", "A113177", "A120007", "A224787", "A276085", "A289142", "A335657", "A341885", "A356163", "A373149", "A373158", "A373371" ]
[ "M0461", "N0168" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001414.seq
1b9cd386d69e32b1da3ad09e024ddb0f
A001415
Number of ways of folding a 2 X n strip of stamps.
[ "1", "2", "8", "60", "320", "1980", "10512", "60788", "320896", "1787904", "9381840", "51081844", "266680992", "1429703548", "7432424160", "39409195740", "204150606976", "1073644675448", "5545305620064", "28980175671212", "149302889205120" ]
[ "nonn", "more" ]
54
0
5
null
[ "M1891", "N0745" ]
N. J. A. Sloane
2025-03-22T11:17:18
oeisdata/seq/A001/A001415.seq
3df3e9e106153b90376d9c1293fd9c5d
A001416
Number of ways of folding a 3 X n strip of stamps.
[ "1", "6", "60", "1368", "15552", "201240", "2016432", "21582624", "201060768", "1944012744", "17257455960", "156760071600", "1346073913440", "11734199738820", "98420246759688" ]
[ "nonn", "hard", "more" ]
36
0
5
[ "A000136", "A000560", "A001415", "A001416", "A001417", "A001418", "A195646" ]
[ "M4271", "N1785" ]
N. J. A. Sloane
2025-03-21T21:57:34
oeisdata/seq/A001/A001416.seq
e7e6bae9133f66b34c1c66a2113916b6
A001417
Number of ways of folding a 2 X 2 X ... X 2 n-dimensional map.
[ "1", "2", "8", "96", "4608", "798720", "361267200", "362794844160" ]
[ "hard", "nonn", "nice", "more" ]
38
0
5
[ "A000136", "A000560", "A001417", "A001418", "A195646" ]
[ "M1901", "N0750" ]
N. J. A. Sloane.
2025-03-21T15:43:14
oeisdata/seq/A001/A001417.seq
ad9c10092cdaa67a13a5e4a30f2df9f3
A001418
Number of ways of folding an n X n sheet of stamps.
[ "1", "8", "1368", "300608", "186086600", "123912532224", "129950723279272" ]
[ "nonn", "hard", "more" ]
54
0
5
[ "A000136", "A000560", "A001417", "A001418", "A195646" ]
[ "M4587", "N1956" ]
N. J. A. Sloane
2025-03-21T15:45:20
oeisdata/seq/A001/A001418.seq
b49cd0b83051245c72444b09919b9698
A001419
Number of n-celled polyominoes with holes.
[ "0", "0", "0", "0", "0", "0", "1", "6", "37", "195", "979", "4663", "21474", "96496", "425449", "1849252", "7946380", "33840946", "143060339", "601165888", "2513617990", "10466220315", "43425174374", "179630865835", "741123699012", "3050860717372", "12534339432498", "51408312232300", "210526591157926", "860989703302456" ]
[ "nonn", "hard" ]
71
0
5
[ "A000104", "A000105", "A001419" ]
[ "M4226", "N1767" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001419.seq
fccef04c1e49231b60ae741324c598e8
A001420
Number of fixed 2-dimensional triangular-celled animals with n cells (n-iamonds, polyiamonds) in the 2-dimensional hexagonal lattice.
[ "2", "3", "6", "14", "36", "94", "250", "675", "1838", "5053", "14016", "39169", "110194", "311751", "886160", "2529260", "7244862", "20818498", "59994514", "173338962", "501994070", "1456891547", "4236446214", "12341035217", "36009329450", "105229462401", "307942754342", "902338712971", "2647263986022", "7775314024683", "22861250676074", "67284446545605" ]
[ "nonn", "hard", "nice" ]
66
0
5
[ "A000577", "A001168", "A001420", "A006534", "A030223", "A030224" ]
[ "M0806", "N0305" ]
N. J. A. Sloane
2024-09-03T11:08:40
oeisdata/seq/A001/A001420.seq
09de558d544cbd52da6acb9e9b286f1e
A001421
a(n) = (6*n)!/((n!)^3*(3*n)!).
[ "1", "120", "83160", "81681600", "93699005400", "117386113965120", "155667030019300800", "214804163196079142400", "305240072216678400087000", "443655767845074392936328000", "656486312795713480715743268160", "985646873056680684690542988249600", "1497786250388951255453847206769124800" ]
[ "nonn" ]
98
0
5
[ "A001421", "A008977", "A008979", "A092870", "A145492", "A145493", "A145494", "A184423", "A184892", "A184896", "A184898", "A289292" ]
null
N. J. A. Sloane, Glenn K Painter (KUPK78A(AT)prodigy.com)
2025-01-23T00:30:43
oeisdata/seq/A001/A001421.seq
1d6d757fdbe4c0004b70c79824c257b7
A001422
Numbers which are not the sum of distinct squares.
[ "2", "3", "6", "7", "8", "11", "12", "15", "18", "19", "22", "23", "24", "27", "28", "31", "32", "33", "43", "44", "47", "48", "60", "67", "72", "76", "92", "96", "108", "112", "128" ]
[ "nonn", "fini", "full", "changed" ]
46
0
5
[ "A001422", "A001476", "A001661", "A003995", "A004441", "A007419", "A025524", "A033461", "A046039", "A053614", "A121405", "A194768", "A194769", "A276517" ]
null
N. J. A. Sloane, Jeff Adams (jeff.adams(AT)byu.net)
2025-04-21T03:45:35
oeisdata/seq/A001/A001422.seq
19b6c2c25c381159792a0e33dcb522f4
A001423
Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
[ "1", "1", "4", "18", "126", "1160", "15973", "836021", "1843120128", "52989400714478", "12418001077381302684" ]
[ "nonn", "hard", "more", "nice" ]
72
0
5
[ "A001423", "A001426", "A023814", "A058107", "A058123", "A151823" ]
[ "M3550", "N1438" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001423.seq
b87a5907e115b9e508a487c5aea8e5a3
A001424
Number of nonisomorphic and nonantiisomorphic groupoids with n elements.
[ "1", "1", "7", "1734", "89521056", "1241763995193675", "7162795001695681351632672", "25488450150907292192918677242007992558", "77841043345568973636021269757801814299054870565039692" ]
[ "nonn" ]
28
0
5
[ "A001329", "A001424", "A029850" ]
[ "M4465", "N1894" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001424.seq
9bcfabbb11a79a5ff861a0ba8ed084f2
A001425
Number of commutative groupoids with n elements.
[ "1", "1", "4", "129", "43968", "254429900", "30468670170912", "91267244789189735259", "8048575431238519331999571800", "24051927835861852500932966021650993560", "2755731922430783367615449408031031255131879354330" ]
[ "nonn" ]
30
0
5
[ "A001329", "A001425", "A023813", "A038016", "A079183" ]
[ "M3714", "N1518" ]
N. J. A. Sloane.
2021-12-19T13:48:48
oeisdata/seq/A001/A001425.seq
34721972a7814695e59e874e63d146d4
A001426
Number of commutative semigroups of order n.
[ "1", "1", "3", "12", "58", "325", "2143", "17291", "221805", "11545843", "3518930337" ]
[ "nonn", "nice", "hard", "more" ]
44
0
5
[ "A001329", "A001423", "A001426", "A023815", "A027851", "A058105", "A058116", "A079193", "A079196", "A079199" ]
[ "M2929", "N1177" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001426.seq
f834c184e807cc7a1ec939139c801466
A001427
Number of regular semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
[ "1", "3", "9", "42", "206", "1352", "10168", "91073", "925044" ]
[ "nonn", "nice", "hard", "more" ]
31
0
5
null
[ "M2823", "N1136" ]
N. J. A. Sloane
2021-12-19T09:00:00
oeisdata/seq/A001/A001427.seq
37904e1c350ff362cade988189b763d7
A001428
Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
[ "1", "2", "5", "16", "52", "208", "911", "4637", "26422", "169163", "1198651", "9324047", "78860687", "719606005", "7035514642" ]
[ "nonn", "nice", "hard", "more" ]
47
0
5
[ "A001428", "A234843", "A234844", "A234845" ]
[ "M1489", "N0586" ]
N. J. A. Sloane
2024-06-03T14:20:17
oeisdata/seq/A001/A001428.seq
d338b2ede9bf0b680343b485f27a34a3
A001429
Number of n-node connected unicyclic graphs.
[ "1", "2", "5", "13", "33", "89", "240", "657", "1806", "5026", "13999", "39260", "110381", "311465", "880840", "2497405", "7093751", "20187313", "57537552", "164235501", "469406091", "1343268050", "3848223585", "11035981711", "31679671920", "91021354454", "261741776369", "753265624291", "2169441973139", "6252511838796" ]
[ "nonn", "nice", "changed" ]
98
0
5
[ "A000055", "A001349", "A001429", "A001434", "A002494", "A005703", "A006129", "A006649", "A014068", "A054548", "A054924", "A057500", "A116508", "A129271", "A133686", "A137916", "A137917", "A137918", "A140637", "A140638", "A236570", "A368983", "A369143", "A369201" ]
[ "M1438", "N0568" ]
N. J. A. Sloane
2025-04-16T05:24:03
oeisdata/seq/A001/A001429.seq
1fd56bd057c1f0b474bf8000f7040926
A001430
Number of graphs with n nodes and n-2 edges.
[ "0", "1", "1", "2", "4", "9", "21", "56", "148", "428", "1305", "4191", "14140", "50159", "185987", "720298", "2905512", "12180208", "52951701", "238253067", "1107432714", "5308573473", "26202267612", "132977762151", "692996060768" ]
[ "nonn", "nice", "easy" ]
28
0
5
[ "A001430", "A008406" ]
[ "M1187", "N0458" ]
N. J. A. Sloane
2018-05-06T13:14:53
oeisdata/seq/A001/A001430.seq
784112a59fb487cce54e2d2190fb907b
A001431
Number of graphs with n nodes and n-3 edges.
[ "0", "0", "1", "1", "2", "5", "10", "24", "63", "165", "467", "1405", "4435", "14775", "51814", "190443", "732472", "2939612", "12277230", "53233295", "239083372", "1109921554", "5316143531", "26225625392", "133050795412", "693227353094", "3704785464812", "20285853687809", "113690627637475", "651559904414667" ]
[ "nonn", "easy" ]
32
0
5
[ "A001431", "A008406" ]
[ "M1382", "N0540" ]
N. J. A. Sloane
2024-07-29T12:36:30
oeisdata/seq/A001/A001431.seq
423df75277b5bd064bdd0db17b64690b
A001432
Number of graphs with n nodes and n-4 edges.
[ "0", "0", "0", "1", "1", "2", "5", "11", "25", "66", "172", "485", "1446", "4541", "15036", "52496", "192218", "737248", "2952621", "12313532", "53336122", "239380403", "1110793092", "5318743428", "26233496486", "133074975399" ]
[ "nonn", "easy" ]
28
0
5
[ "A001432", "A008406" ]
[ "M1397", "N0544" ]
N. J. A. Sloane
2021-12-23T22:59:45
oeisdata/seq/A001/A001432.seq
38c437ed20dc81e9d2c153959d57e517
A001433
Number of graphs with n nodes and n-1 edges.
[ "1", "1", "1", "3", "6", "15", "41", "115", "345", "1103", "3664", "12763", "46415", "175652", "691001", "2821116", "11932174", "52211412", "236007973", "1100528508", "5287050500", "26134330813", "132760735671", "692294900849", "3701754158688", "20275893222445", "113657560920970", "651449039159673", "3814790900995022", "22805438484189851" ]
[ "nonn", "easy", "nice" ]
35
0
5
[ "A001433", "A008406" ]
[ "M2588", "N1024" ]
N. J. A. Sloane
2022-08-18T10:21:39
oeisdata/seq/A001/A001433.seq
13026a3bd6c1a3a3ae6bc83358394cbf
A001434
Number of graphs with n nodes and n edges.
[ "1", "0", "0", "1", "2", "6", "21", "65", "221", "771", "2769", "10250", "39243", "154658", "628635", "2632420", "11353457", "50411413", "230341716", "1082481189", "5228952960", "25945377057", "132140242356", "690238318754", "3694876952577", "20252697246580", "113578669178222", "651178533855913", "3813856010041981" ]
[ "nonn", "easy", "nice", "changed" ]
45
0
5
[ "A000055", "A000088", "A001187", "A001349", "A001429", "A001434", "A002494", "A005703", "A006125", "A006129", "A006649", "A008406", "A014068", "A054924", "A057500", "A116508", "A137916", "A137917", "A236570", "A367863", "A368598", "A368983", "A369192", "A369201", "A370315" ]
[ "M1653", "N0647" ]
N. J. A. Sloane
2025-04-17T03:37:43
oeisdata/seq/A001/A001434.seq
459ab29d7e1d94932211dafdc869ce7b
A001435
Number of connected graphs with n nodes and n+1 edges.
[ "0", "0", "0", "1", "5", "19", "67", "236", "797", "2678", "8833", "28908", "93569", "300748", "959374", "3042808", "9597679", "30134509", "94218306", "293509092", "911325798", "2821327949", "8711297753", "26833501800", "82476837698", "253007383067", "774737986836" ]
[ "nonn" ]
35
0
5
[ "A000055", "A001429", "A001435", "A076263" ]
[ "M3889", "N1597" ]
N. J. A. Sloane
2023-02-16T09:54:57
oeisdata/seq/A001/A001435.seq
97257a710b5e16da7cfad9b6ad93ea07
A001436
Number of connected graphs with n nodes, n+2 edges.
[ "0", "0", "0", "1", "4", "22", "107", "486", "2075", "8548", "33851", "130365", "489387", "1799700", "6499706", "23118465", "81134475", "281454170", "966388692", "3288208176", "11098235911", "37188198356", "123800999503", "409715126169", "1348690034859", "4417932007626", "14407260221164" ]
[ "nonn" ]
21
0
5
[ "A001436", "A054923" ]
[ "M3583", "N1453" ]
N. J. A. Sloane
2021-05-05T18:00:08
oeisdata/seq/A001/A001436.seq
c47b1814d2615cb58d081f7082efa39f
A001437
Number of connected graphs with n nodes and ceiling(n(n-1)/4) edges.
[ "1", "1", "2", "5", "22", "138", "1579", "33366", "1348674", "105925685", "15968704512", "4520384306832", "2402814904220039", "2425664021535713098", "4647586298937784001491", "16787189663016572148130262", "114716901953374968257425111039" ]
[ "nonn", "nice" ]
21
0
5
[ "A001437", "A054924" ]
[ "M1538", "N0601" ]
N. J. A. Sloane.
2018-05-06T13:15:43
oeisdata/seq/A001/A001437.seq
1eb82392b190f4fcf149bda3fc3a0d10
A001438
Maximal number of mutually orthogonal Latin squares (or MOLS) of order n.
[ "1", "2", "3", "4", "1", "6", "7", "8" ]
[ "nonn", "hard", "more", "nice" ]
86
0
5
[ "A001438", "A287695", "A328873" ]
null
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001438.seq
eb203a7117f35c163d2b303dcd539da2
A001439
Number of proper linear spaces of order n.
[ "0", "0", "0", "0", "1", "0", "1", "1", "1", "3", "7", "1", "120", "398" ]
[ "nonn", "hard" ]
16
0
5
[ "A001439", "A031436" ]
null
N. J. A. Sloane
2023-01-14T03:06:17
oeisdata/seq/A001/A001439.seq
f5284fcd4222706543b3673d36cfaa88
A001440
Number of symmetric Costas arrays of order n that are inequivalent under dihedral group.
[ "1", "1", "1", "1", "2", "5", "10", "9", "10", "14", "18", "17", "25", "23", "31", "20", "19", "10", "6", "4", "8", "5", "10", "0", "2", "2", "7", "0", "5", "4", "0", "0" ]
[ "nonn", "hard", "more" ]
11
0
5
[ "A001440", "A001441", "A001442", "A008404" ]
null
N. J. A. Sloane
2022-02-01T23:57:07
oeisdata/seq/A001/A001440.seq
c935a0d6f2cce99f96b59dc7ffb6b819
A001441
Number of inequivalent Costas arrays of order n under dihedral group.
[ "1", "1", "1", "2", "6", "17", "30", "60", "100", "277", "555", "990", "1616", "2168", "2467", "2648", "2294", "1892", "1283", "810", "446", "259", "114", "25", "12", "8", "29", "89", "23" ]
[ "nonn", "hard", "more", "nice" ]
19
0
5
[ "A001440", "A001441", "A001442", "A008403", "A008404" ]
null
N. J. A. Sloane.
2017-04-11T04:51:23
oeisdata/seq/A001/A001441.seq
8261579f3fbe4f52bff47f4b7e5765a5
A001442
G-symmetric Costas arrays of order n that are inequivalent under dihedral group.
[ "1", "1", "0", "2", "1", "4", "0", "3", "0", "24", "0", "44", "4", "31", "0", "77", "0", "29", "0", "3", "0", "55", "0" ]
[ "nonn", "hard", "more", "nice" ]
8
0
5
[ "A001440", "A001441", "A001442", "A008403", "A008404" ]
null
N. J. A. Sloane.
2012-06-08T07:23:37
oeisdata/seq/A001/A001442.seq
eaa7e83bbc0eec8d01258b8b15607d39
A001443
Number of strong starters in cyclic group of order 2n+1.
[ "0", "0", "2", "0", "4", "8", "32", "224", "800", "6660", "27554", "158680", "1201626", "9415980", "76761968", "672858900", "6015305136", "59514095596" ]
[ "nonn", "more" ]
22
0
5
[ "A001443", "A006205" ]
null
N. J. A. Sloane
2024-08-05T13:51:59
oeisdata/seq/A001/A001443.seq
16dde0f343c9bf1388c6e49032667d1b
A001444
Bending a piece of wire of length n+1 (configurations that can only be brought into coincidence by turning the figure over are counted as different).
[ "1", "2", "6", "15", "45", "126", "378", "1107", "3321", "9882", "29646", "88695", "266085", "797526", "2392578", "7175547", "21526641", "64573362", "193720086", "581140575", "1743421725", "5230206126", "15690618378", "47071677987", "141215033961", "423644570442", "1270933711326", "3812799539655", "11438398618965" ]
[ "nonn", "nice", "easy" ]
51
0
5
[ "A000244", "A001444", "A001997", "A001998" ]
null
Todd Simpson
2024-03-25T17:13:35
oeisdata/seq/A001/A001444.seq
9c85403f57027bf19a0467eca6dff637
A001445
a(n) = (2^n + 2^[ n/2 ] )/2.
[ "3", "5", "10", "18", "36", "68", "136", "264", "528", "1040", "2080", "4128", "8256", "16448", "32896", "65664", "131328", "262400", "524800", "1049088", "2098176", "4195328", "8390656", "16779264", "33558528", "67112960", "134225920", "268443648" ]
[ "nonn" ]
31
0
5
[ "A001445", "A052957", "A056309" ]
null
N. J. A. Sloane
2021-09-12T18:01:15
oeisdata/seq/A001/A001445.seq
915f210b5a14930f164644d57c7ca375
A001446
a(n) = (4^n + 4^[ n/2 ] )/2.
[ "10", "34", "136", "520", "2080", "8224", "32896", "131200", "524800", "2097664", "8390656", "33556480", "134225920", "536879104", "2147516416", "8589967360", "34359869440", "137439084544", "549756338176", "2199023779840", "8796095119360" ]
[ "nonn", "easy" ]
18
0
5
[ "A001445", "A001446", "A056450" ]
null
N. J. A. Sloane
2022-02-01T23:58:35
oeisdata/seq/A001/A001446.seq
60c90cf48686429467879ca0266d8a0c
A001447
a(n) = (5^n + 5^floor(n/2))/2.
[ "1", "3", "15", "65", "325", "1575", "7875", "39125", "195625", "976875", "4884375", "24415625", "122078125", "610359375", "3051796875", "15258828125", "76294140625", "381469921875", "1907349609375", "9536744140625", "47683720703125" ]
[ "nonn", "easy" ]
22
0
5
null
null
N. J. A. Sloane
2022-02-02T03:58:58
oeisdata/seq/A001/A001447.seq
703aa65e0614746c627126fc9bcc1168
A001448
a(n) = binomial(4n,2n) or (4*n)!/((2*n)!*(2*n)!).
[ "1", "6", "70", "924", "12870", "184756", "2704156", "40116600", "601080390", "9075135300", "137846528820", "2104098963720", "32247603683100", "495918532948104", "7648690600760440", "118264581564861424", "1832624140942590534", "28453041475240576740", "442512540276836779204", "6892620648693261354600" ]
[ "nonn", "nice", "easy" ]
134
0
5
[ "A000984", "A001448", "A002458", "A066357", "A091527", "A211419", "A211421", "A262732", "A262733" ]
null
N. J. A. Sloane
2025-02-08T14:24:13
oeisdata/seq/A001/A001448.seq
0e2fcc52401bf9242ba07f47d89f0892
A001449
Binomial coefficients binomial(5n,n).
[ "1", "5", "45", "455", "4845", "53130", "593775", "6724520", "76904685", "886163135", "10272278170", "119653565850", "1399358844975", "16421073515280", "193253756909160", "2280012686716080", "26958221130508525" ]
[ "nonn", "easy" ]
55
0
5
[ "A000984", "A001449", "A004355", "A004368", "A004381", "A005809", "A005810", "A169958", "A169961" ]
null
N. J. A. Sloane
2024-10-31T01:33:00
oeisdata/seq/A001/A001449.seq
598dfaf22f18eceaa13dea6a075c36a0
A001450
a(n) = binomial(5*n,2*n).
[ "1", "10", "210", "5005", "125970", "3268760", "86493225", "2319959400", "62852101650", "1715884494940", "47129212243960", "1300853625660225", "36052387482172425", "1002596421878664480", "27963143931814663880", "781879430625942976880", "21910242651571684460050", "615167304833936727234180" ]
[ "nonn", "easy" ]
62
0
5
[ "A000108", "A001450", "A001451", "A001459", "A001460", "A060941", "A066802", "A259550" ]
null
N. J. A. Sloane
2024-06-12T17:34:46
oeisdata/seq/A001/A001450.seq
8f649adef3cf2a1633447e36530172bb
A001451
a(n) = (5*n)!/((3*n)!*n!*n!).
[ "1", "20", "1260", "100100", "8817900", "823727520", "79919739900", "7962100660800", "808906548235500", "83426304143982800", "8707404737345073760", "917663774856743842200", "97491279924241456098300", "10427604345391237790688000", "1121786259855036145008408000" ]
[ "nonn", "easy", "walk" ]
48
0
5
[ "A000897", "A001451", "A002894", "A002897", "A006480", "A008977", "A186420", "A188662", "A273628", "A273629" ]
null
N. J. A. Sloane
2024-10-16T09:23:18
oeisdata/seq/A001/A001451.seq
7a13a61c107f559d39799ab0a3d5d1aa
A001452
Number of 5-line partitions of n.
[ "1", "1", "3", "6", "13", "24", "47", "83", "152", "263", "457", "768", "1292", "2118", "3462", "5564", "8888", "14016", "21973", "34081", "52552", "80331", "122078", "184161", "276303", "411870", "610818", "900721", "1321848", "1929981", "2805338", "4058812", "5847966", "8390097", "11990531", "17069145", "24210571", "34215537", "48190451", "67644522" ]
[ "nonn" ]
53
0
5
[ "A000041", "A000990", "A000991", "A001452", "A002799", "A225196", "A225197", "A225198", "A225199", "A242641" ]
[ "M2564", "N1015" ]
N. J. A. Sloane
2023-10-27T19:13:34
oeisdata/seq/A001/A001452.seq
1caae332a7d4c6fd9dbe5a6ceaac172f
A001453
Catalan numbers - 1.
[ "1", "4", "13", "41", "131", "428", "1429", "4861", "16795", "58785", "208011", "742899", "2674439", "9694844", "35357669", "129644789", "477638699", "1767263189", "6564120419", "24466267019", "91482563639", "343059613649", "1289904147323", "4861946401451", "18367353072151", "69533550916003", "263747951750359" ]
[ "nonn", "easy" ]
98
0
5
[ "A000108", "A001453", "A001454", "A047874", "A120304", "A141364", "A246604", "A273526", "A289615", "A289616", "A289652", "A289653", "A289654" ]
[ "M3464", "N1409" ]
N. J. A. Sloane
2023-10-27T19:12:30
oeisdata/seq/A001/A001453.seq
73d6ec99a097e60f6ba2bd87768734c6
A001454
Number of permutations of length n with longest increasing subsequence of length 3.
[ "1", "9", "61", "381", "2332", "14337", "89497", "569794", "3704504", "24584693", "166335677", "1145533650", "8017098273", "56928364553", "409558170361", "2981386305018", "21935294881644", "162951791097669", "1221201051018189", "9225637750090023", "70209505971502533", "537934326588404973" ]
[ "nonn" ]
39
0
5
[ "A001453", "A001454", "A047874" ]
[ "M4640", "N1983" ]
N. J. A. Sloane
2022-02-03T05:55:46
oeisdata/seq/A001/A001454.seq
e4eb4879341bf6bdc3ed597e9b5a5322
A001455
Number of permutations of length n with longest increasing subsequence of length 4.
[ "1", "16", "181", "1821", "17557", "167449", "1604098", "15555398", "153315999", "1538907306", "15743413076", "164161815768", "1744049683213", "18865209953045", "207591285198178", "2321616416280982", "26362085777156567", "303635722412859447", "3544040394934246209", "41881891423602685193" ]
[ "nonn" ]
34
0
5
[ "A001455", "A047874" ]
[ "M5016", "N2161" ]
N. J. A. Sloane
2022-02-03T00:50:24
oeisdata/seq/A001/A001455.seq
0aa7d0b3cfa3164be5e32cd5a73727e0
A001456
Number of permutations of length n with longest increasing subsequence of length 5.
[ "1", "25", "421", "6105", "83029", "1100902", "14516426", "192422979", "2579725656", "35098717902", "485534447114", "6835409506841", "97966603326993", "1429401763567226", "21226755241285022", "320692032888290224", "4926576077469905280", "76913478420068425515", "1219520974164038038455" ]
[ "nonn" ]
38
0
5
[ "A001456", "A047874" ]
[ "M5183", "N2251" ]
N. J. A. Sloane
2023-10-27T19:11:58
oeisdata/seq/A001/A001456.seq
b3b3455a4a07dbb8c0aef4b76aad63f4
A001457
Number of permutations of length n with longest increasing subsequence of length 6.
[ "1", "36", "841", "16465", "296326", "5122877", "87116283", "1477363967", "25191909848", "434119587475", "7583461369373", "134533482045389", "2426299018270338", "44506885647682026", "830512607486659272", "15764082963927084216", "304295666452406076997", "5971518739677370493811" ]
[ "nonn" ]
40
0
5
[ "A001457", "A047874" ]
[ "M5256", "N2288" ]
N. J. A. Sloane
2023-10-27T19:12:11
oeisdata/seq/A001/A001457.seq
471e79b45055c28af575f6e113c3943b
A001458
Number of permutations of length n with longest increasing subsequence of length 7.
[ "1", "49", "1513", "38281", "874886", "18943343", "399080475", "8312317976", "172912977525", "3615907795025", "76340522760097", "1631788075873114", "35378058306185002", "778860477345867008", "17423197016288134608", "396169070839236609236", "9157097111888617643722", "215143361542096212159897" ]
[ "nonn" ]
41
0
5
[ "A001458", "A047874" ]
[ "M5297", "N2304" ]
N. J. A. Sloane
2023-10-27T19:12:48
oeisdata/seq/A001/A001458.seq
5fbba42cb26f198e7dd0d14032adddf7
A001459
a(n) = (5*n)!/((2*n)!*(2*n)!*n!).
[ "1", "30", "3150", "420420", "62355150", "9816086280", "1605660228900", "269764879032000", "46225898052627150", "8042050347997165500", "1415997888807961859400", "251762943910387780962000", "45125969443194371927422500", "8143514687130622653091029120", "1478138194032735032800001630400" ]
[ "nonn" ]
36
0
5
[ "A001459", "A006480" ]
null
N. J. A. Sloane
2022-02-03T00:51:09
oeisdata/seq/A001/A001459.seq
246e4b92cda629710b4c59d9559ee7c8
A001460
a(n) = (5*n)!/((2*n)!*(n!)^3).
[ "1", "60", "18900", "8408400", "4364860500", "2473653742560", "1483630051503600", "925833064837824000", "594927307937311420500", "391004487919622186610000", "261614105944603801295306400", "177601637048592673099585584000", "122027661025630720013771117910000" ]
[ "nonn" ]
52
0
5
[ "A000984", "A001460", "A008978", "A268545", "A268555" ]
null
N. J. A. Sloane
2023-09-04T02:01:16
oeisdata/seq/A001/A001460.seq
a2b812062b84e25b11599c7220a81fd2
A001461
Partial sums of A006206.
[ "1", "2", "3", "4", "6", "8", "12", "17", "25", "36", "54", "79", "119", "177", "267", "402", "612", "928", "1420", "2170", "3334", "5125", "7911", "12216", "18926", "29346", "45610", "70960", "110610", "172577", "269685", "421830", "660648", "1035603", "1625123" ]
[ "nonn", "nice", "easy" ]
29
0
5
null
null
N. J. A. Sloane, David Broadhurst
2020-04-22T18:30:19
oeisdata/seq/A001/A001461.seq
d1e6774440631171d3b876544b0dca3a
A001462
Golomb's sequence: a(n) is the number of times n occurs, starting with a(1) = 1.
[ "1", "2", "2", "3", "3", "4", "4", "4", "5", "5", "5", "6", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "18", "19" ]
[ "easy", "nonn", "nice", "core" ]
185
0
5
[ "A000002", "A001462", "A001463", "A013189", "A013322", "A080605", "A080606", "A080607", "A088517", "A095114", "A109167", "A169682", "A250983", "A262986", "A319434" ]
[ "M0257", "N0091" ]
N. J. A. Sloane
2025-03-05T09:03:18
oeisdata/seq/A001/A001462.seq
6590bb2f2b61d1a11dccf926fd51200a
A001463
Partial sums of A001462; also a(n) is the last occurrence of n in A001462.
[ "1", "3", "5", "8", "11", "15", "19", "23", "28", "33", "38", "44", "50", "56", "62", "69", "76", "83", "90", "98", "106", "114", "122", "131", "140", "149", "158", "167", "177", "187", "197", "207", "217", "228", "239", "250", "261", "272", "284", "296", "308", "320", "332", "344", "357", "370", "383", "396", "409", "422", "436", "450", "464", "478", "492", "506", "521", "536", "551", "566", "581", "596" ]
[ "nonn", "easy", "nice" ]
49
0
5
null
[ "M2438", "N0965" ]
N. J. A. Sloane
2022-04-13T13:25:15
oeisdata/seq/A001/A001463.seq
6ee2a036dc02612cda8fbea201b697cd
A001464
Expansion of e.g.f. exp(-x - (1/2)*x^2).
[ "1", "-1", "0", "2", "-2", "-6", "16", "20", "-132", "-28", "1216", "-936", "-12440", "23672", "138048", "-469456", "-1601264", "9112560", "18108928", "-182135008", "-161934624", "3804634784", "-404007680", "-83297957568", "92590134208", "1906560847424", "-4221314202624", "-45349267830400", "159324751301248" ]
[ "sign", "easy" ]
101
0
5
[ "A000085", "A000178", "A001147", "A001464", "A066325", "A069834", "A099174", "A200675", "A252284", "A369755", "A369756" ]
[ "M0361", "N0137" ]
N. J. A. Sloane, J. H. Conway and Simon Plouffe
2025-02-16T08:32:23
oeisdata/seq/A001/A001464.seq
12b60205261d48e512a5198da7b51c09
A001465
Number of degree-n odd permutations of order 2.
[ "0", "0", "1", "3", "6", "10", "30", "126", "448", "1296", "4140", "17380", "76296", "296088", "1126216", "4940040", "23904000", "110455936", "489602448", "2313783216", "11960299360", "61878663840", "309644323296", "1587272962528", "8699800221696", "48793502304000", "268603261201600", "1487663739072576" ]
[ "nonn" ]
55
0
5
[ "A000085", "A000704", "A001465" ]
[ "M2538", "N1003" ]
N. J. A. Sloane and J. H. Conway
2020-10-24T04:28:10
oeisdata/seq/A001/A001465.seq
2d642dc6658a1636370a4dbe6b92794c
A001466
Denominators of greedy Egyptian fraction expansion of Pi - 3.
[ "8", "61", "5020", "128541455", "162924332716605980", "28783052231699298507846309644849796", "871295615653899563300996782209332544845605756266650946342214549769447" ]
[ "nonn", "frac" ]
67
0
5
[ "A001466", "A006525", "A182257", "A224230" ]
[ "M4553", "N1935" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001466.seq
1d072da41bde13e78d7f4d169a2b9083
A001467
Denominators of an expansion for Pi.
[ "1", "1", "1", "7", "-791", "-3748629", "151648960887729", "-1323497544567561138595307148089", "41444465282455711991644958522615049159671653083333293470875123" ]
[ "sign", "frac" ]
27
0
5
[ "A001466", "A001467", "A014013", "A073422" ]
[ "M4464", "N1893" ]
N. J. A. Sloane
2015-03-07T11:55:54
oeisdata/seq/A001/A001467.seq
cdc79d57cf1a6f8bf962b96dd5984652
A001468
There are a(n) 2's between successive 1's.
[ "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2" ]
[ "nonn", "easy", "nice" ]
102
0
5
[ "A000201", "A001030", "A001468", "A001950", "A003622", "A003842", "A003849", "A004641", "A005614", "A014675", "A022342", "A088462", "A096270", "A114986", "A124841", "A280511" ]
[ "M0099", "N0036" ]
N. J. A. Sloane
2022-08-26T10:26:17
oeisdata/seq/A001/A001468.seq
3bb82134e4eeb3279fd5288dd0840a98
A001469
Genocchi numbers (of first kind); unsigned coefficients give expansion of x*tan(x/2).
[ "-1", "1", "-3", "17", "-155", "2073", "-38227", "929569", "-28820619", "1109652905", "-51943281731", "2905151042481", "-191329672483963", "14655626154768697", "-1291885088448017715", "129848163681107301953", "-14761446733784164001387", "1884515541728818675112649", "-268463531464165471482681379" ]
[ "sign", "easy", "nice" ]
194
0
5
[ "A000182", "A001469", "A006846", "A012509", "A065547", "A110501", "A226158", "A297703" ]
[ "M3041", "N1233" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001469.seq
dfb5c907b71c15feff4936dddbcebf93
A001470
Number of degree-n permutations of order dividing 3.
[ "1", "1", "1", "3", "9", "21", "81", "351", "1233", "5769", "31041", "142011", "776601", "4874013", "27027729", "168369111", "1191911841", "7678566801", "53474964993", "418199988339", "3044269834281", "23364756531621", "199008751634001", "1605461415071823", "13428028220072049", "123280859122040601" ]
[ "easy", "nonn", "nice" ]
72
0
5
[ "A000085", "A001470", "A001472", "A008307" ]
[ "M2782", "N1118" ]
N. J. A. Sloane, J. H. Conway and Simon Plouffe
2025-03-13T16:26:50
oeisdata/seq/A001/A001470.seq
4584b7226070d301297651cc004d0754
A001471
Number of degree-n permutations of order exactly 3.
[ "0", "0", "0", "2", "8", "20", "80", "350", "1232", "5768", "31040", "142010", "776600", "4874012", "27027728", "168369110", "1191911840", "7678566800", "53474964992", "418199988338", "3044269834280", "23364756531620", "199008751634000", "1605461415071822" ]
[ "nonn", "easy", "nice" ]
38
0
5
[ "A000085", "A001189", "A001470", "A001471", "A001472", "A001473", "A052501", "A053496", "A053505", "A057731", "A061121", "A061128" ]
[ "M1833", "N0727" ]
N. J. A. Sloane and J. H. Conway
2024-03-09T17:18:06
oeisdata/seq/A001/A001471.seq
6d1c6c8a6c6fa19f675f4498adaef626
A001472
Number of degree-n permutations of order dividing 4.
[ "1", "1", "2", "4", "16", "56", "256", "1072", "6224", "33616", "218656", "1326656", "9893632", "70186624", "574017536", "4454046976", "40073925376", "347165733632", "3370414011904", "31426411211776", "328454079574016", "3331595921852416", "37125035407900672", "400800185285464064" ]
[ "nonn", "nice", "easy" ]
56
0
5
[ "A000085", "A001470", "A001472", "A008307", "A053495" ]
[ "M1292", "N0495" ]
N. J. A. Sloane and J. H. Conway
2024-12-27T00:44:58
oeisdata/seq/A001/A001472.seq
c1f2a02be49e979fa6499fbe044c1e48
A001473
Number of degree-n permutations of order exactly 4.
[ "0", "0", "0", "6", "30", "180", "840", "5460", "30996", "209160", "1290960", "9753480", "69618120", "571627056", "4443697440", "40027718640", "346953934320", "3369416698080", "31421601510336", "328430320909920", "3331475969159520", "37124416523261760" ]
[ "nonn" ]
24
0
5
[ "A000085", "A001189", "A001470", "A001471", "A001472", "A001473", "A052501", "A053496", "A053505", "A057731", "A061121", "A061128" ]
[ "M4206", "N1756" ]
N. J. A. Sloane and J. H. Conway
2022-09-08T08:44:29
oeisdata/seq/A001/A001473.seq
d0fbe4600dd5cd099f6c80f2680077e6
A001474
w such that w^3+x^3+y^3+z^3=0, w>|x|>|y|>|z|, is soluble.
[ "6", "9", "12", "16", "19", "20", "25", "27", "28", "29", "34", "39", "40", "41", "44", "46", "51", "53", "54", "55", "58", "60", "67", "69", "70", "71", "72", "75", "76", "80", "81", "82", "84", "85", "87", "88", "89", "90", "93", "94", "96", "97", "98", "99", "102", "103", "105", "108", "109", "110", "111", "113", "115", "116", "120", "121", "122", "123", "126", "127", "129", "132", "134", "137", "139" ]
[ "nonn", "nice" ]
17
0
5
[ "A001235", "A001474" ]
null
N. J. A. Sloane
2022-08-06T03:02:46
oeisdata/seq/A001/A001474.seq
6c7deee8345cb6e0a8bc0bb04f9d3fea
A001475
a(n) = a(n-1) + n * a(n-2), where a(1) = 1, a(2) = 2.
[ "1", "2", "5", "13", "38", "116", "382", "1310", "4748", "17848", "70076", "284252", "1195240", "5174768", "23103368", "105899656", "498656912", "2404850720", "11879332048", "59976346448", "309442319456", "1628921941312", "8746095288800", "47840221880288", "266492604100288", "1510338372987776" ]
[ "nonn" ]
63
0
5
[ "A000085", "A001189", "A001475", "A013989", "A076276", "A248475" ]
[ "M1449", "N0573" ]
N. J. A. Sloane
2024-11-27T11:50:36
oeisdata/seq/A001/A001475.seq
decb8338e098f909390902ff8732a485
A001476
Numbers that are not the sum of distinct positive cubes.
[ "2", "3", "4", "5", "6", "7", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "29", "30", "31", "32", "33", "34", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "66", "67", "68", "69", "70", "71", "74", "75", "76", "77", "78", "79", "80" ]
[ "nonn", "fini", "full" ]
51
0
5
[ "A001422", "A001476", "A003997", "A279329", "A279486" ]
null
Jeff Adams (jeff.adams(AT)byu.net)
2025-02-16T08:32:23
oeisdata/seq/A001/A001476.seq
22a6754f030c2bdbbca37336e546f353
A001477
The nonnegative integers.
[ "0", "1", "2", "3", "4", "5", "6", "7", "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", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77" ]
[ "core", "nonn", "easy", "mult", "tabl" ]
304
0
5
[ "A000012", "A000027", "A000096", "A000124", "A000217", "A000290", "A000579", "A000737", "A001477", "A001787", "A002412", "A005843", "A008585", "A008586", "A034856", "A038608", "A045943", "A046691", "A052905", "A055112", "A055998", "A055999", "A057427", "A061579", "A102860", "A115067", "A145018", "A152948", "A152950", "A154286", "A166136", "A167487", "A167499", "A185787", "A231179", "A245422" ]
null
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001477.seq
b6509df89cf8189b8a1bfecb19094b4b
A001478
The negative integers.
[ "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-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", "-33", "-34", "-35", "-36", "-37", "-38", "-39", "-40", "-41", "-42", "-43", "-44", "-45", "-46", "-47", "-48", "-49", "-50", "-51", "-52", "-53", "-54", "-55", "-56", "-57", "-58", "-59", "-60", "-61", "-62", "-63", "-64", "-65" ]
[ "core", "sign", "easy" ]
37
0
5
[ "A000027", "A001057", "A001477", "A001478", "A001489", "A130472" ]
null
N. J. A. Sloane
2022-11-14T00:37:49
oeisdata/seq/A001/A001478.seq
cd9c6a93c5ddf0f18bc254b7d8b198a9
A001479
Let p = A007645(n) be the n-th generalized cuban prime and write p = x^2 + 3*y^2; a(n) = x.
[ "0", "2", "1", "4", "2", "5", "4", "7", "8", "5", "2", "7", "10", "1", "10", "8", "2", "7", "4", "13", "1", "14", "8", "14", "11", "7", "14", "13", "16", "8", "11", "16", "17", "7", "2", "19", "4", "17", "19", "11", "1", "14", "5", "10", "22", "16", "4", "23", "20", "8", "23", "13", "10", "5", "16", "22", "20", "19", "25", "4", "11", "22", "25", "8", "26", "13", "1", "28", "28", "26", "23", "29", "28" ]
[ "nonn", "easy", "nice" ]
40
0
5
[ "A000196", "A001479", "A001480", "A007645", "A010052", "A033428" ]
[ "M0166", "N0065" ]
N. J. A. Sloane
2017-02-07T11:39:54
oeisdata/seq/A001/A001479.seq
936b43e64a718a8331915f2587c64b4b
A001480
Let p = A007645(n) be the n-th generalized cuban prime and write p = x^2 + 3*y^2; a(n) = y.
[ "1", "1", "2", "1", "3", "2", "3", "2", "1", "4", "5", "4", "1", "6", "3", "5", "7", "6", "7", "2", "8", "1", "7", "3", "6", "8", "5", "6", "3", "9", "8", "5", "4", "10", "11", "2", "11", "6", "4", "10", "12", "9", "12", "11", "1", "9", "13", "2", "7", "13", "4", "12", "13", "14", "11", "7", "9", "10", "4", "15", "14", "9", "6", "15", "5", "14", "16", "1", "3", "7", "10", "2", "5", "14", "17", "13", "9", "16", "17" ]
[ "nonn", "easy", "nice" ]
36
0
5
[ "A001479", "A001480", "A007645" ]
[ "M0142", "N0057" ]
N. J. A. Sloane
2017-02-07T11:40:27
oeisdata/seq/A001/A001480.seq
016e4026931afcae852e00bcd5bebb3e
A001481
Numbers that are the sum of 2 squares.
[ "0", "1", "2", "4", "5", "8", "9", "10", "13", "16", "17", "18", "20", "25", "26", "29", "32", "34", "36", "37", "40", "41", "45", "49", "50", "52", "53", "58", "61", "64", "65", "68", "72", "73", "74", "80", "81", "82", "85", "89", "90", "97", "98", "100", "101", "104", "106", "109", "113", "116", "117", "121", "122", "125", "128", "130", "136", "137", "144", "145", "146", "148", "149", "153", "157", "160" ]
[ "nonn", "nice", "easy", "core" ]
252
0
5
[ "A000161", "A000290", "A000378", "A000404", "A000415", "A001481", "A002654", "A002828", "A004018", "A022544", "A025284", "A025320", "A046711", "A055025", "A057961", "A064533", "A077773", "A091072", "A118882", "A125022", "A125110", "A232499", "A336820", "A363763" ]
[ "M0968", "N0361" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001481.seq
cb34d602a0189564acd4ae5b865d8359
A001482
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^4 in powers of x.
[ "1", "-4", "6", "-4", "-3", "12", "-16", "16", "-6", "-8", "18", "-28", "26", "-20", "2", "12", "-23", "32", "-36", "28", "-6", "4", "22", "-20", "39", "-32", "32", "-12", "2", "16", "-12", "24", "-40", "28", "-34", "0", "-6", "-16", "0", "-40", "6", "-36", "26", "-32", "-5", "0", "-20", "8", "-16", "12", "-10", "40", "-22", "12", "14", "12", "45", "16", "38", "4", "12", "0", "34", "8", "38", "12", "-24", "44", "2", "16" ]
[ "sign" ]
30
0
5
[ "A001482", "A001483", "A001488", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M3263", "N1317" ]
N. J. A. Sloane
2023-09-04T06:07:55
oeisdata/seq/A001/A001482.seq
d8d3725c4cb33a16eb6427987a442bef
A001483
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^5 in powers of x.
[ "1", "-5", "10", "-10", "0", "19", "-35", "40", "-25", "-10", "45", "-75", "80", "-60", "15", "45", "-85", "115", "-115", "90", "-21", "-35", "95", "-130", "135", "-135", "70", "-35", "-65", "105", "-146", "120", "-150", "90", "-65", "-25", "90", "-115", "150", "-125", "130", "-45", "80", "35", "-5", "160", "-110", "170", "-85", "95", "25", "50", "0", "-60", "95", "-116", "120", "-135" ]
[ "sign" ]
29
0
5
[ "A001482", "A001483", "A001484", "A001488", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M3791", "N1546" ]
N. J. A. Sloane
2023-09-04T06:09:00
oeisdata/seq/A001/A001483.seq
fafc48c1354be9c34a96da810e1ef1ca
A001484
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^6 in powers of x.
[ "1", "-6", "15", "-20", "9", "24", "-65", "90", "-75", "6", "90", "-180", "220", "-180", "66", "110", "-264", "360", "-365", "264", "-66", "-178", "375", "-510", "496", "-414", "180", "60", "-330", "570", "-622", "582", "-390", "220", "96", "-300", "621", "-630", "705", "-492", "300", "0", "-235", "420", "-570", "594", "-735", "420", "-420", "-120", "219", "-586", "360" ]
[ "sign" ]
28
0
5
[ "A001482", "A001483", "A001484", "A001485", "A001488", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M4107", "N1704" ]
N. J. A. Sloane
2023-09-04T06:05:02
oeisdata/seq/A001/A001484.seq
5f8325a91a84f09203203962ebea9354
A001485
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^7 in powers of x.
[ "1", "-7", "21", "-35", "28", "21", "-105", "181", "-189", "77", "140", "-385", "546", "-511", "252", "203", "-693", "1029", "-1092", "798", "-203", "-581", "1281", "-1708", "1687", "-1232", "413", "602", "-1485", "2233", "-2366", "2009", "-1099", "14", "1099", "-2072", "2667", "-2807", "2254", "-1477", "0", "1057", "-2346", "2744", "-3017", "2457" ]
[ "sign" ]
25
0
5
[ "A001482", "A001483", "A001484", "A001485", "A001486", "A001487", "A001488", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M4371", "N1835" ]
N. J. A. Sloane
2023-09-04T06:08:21
oeisdata/seq/A001/A001485.seq
8d4a3bfe981e10f480c7743c55332597
A001486
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^8 in powers of x.
[ "1", "-8", "28", "-56", "62", "0", "-148", "328", "-419", "280", "140", "-728", "1232", "-1336", "848", "224", "-1582", "2688", "-3072", "2408", "-742", "-1568", "3836", "-5264", "5306", "-3744", "924", "2576", "-5686", "7792", "-8092", "6272", "-2751", "-1848", "6008", "-9296", "10556", "-9800", "6692", "-2240", "-3206", "8168", "-11524" ]
[ "sign" ]
25
0
5
[ "A001482", "A001485", "A001486", "A001487", "A001488", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M4502", "N1906" ]
N. J. A. Sloane
2023-09-05T01:21:22
oeisdata/seq/A001/A001486.seq
9e58bb383bea26c75686adbcbb9f004c
A001487
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^9 in powers of x.
[ "1", "-9", "36", "-84", "117", "-54", "-177", "540", "-837", "755", "-54", "-1197", "2535", "-3204", "2520", "-246", "-3150", "6426", "-8106", "7011", "-2844", "-3549", "10359", "-15120", "15804", "-11403", "2574", "8610", "-18972", "25425", "-25824", "18954", "-6165", "-10080", "25101", "-35262", "37799", "-31374", "17379", "1929" ]
[ "sign" ]
23
0
5
[ "A001482", "A001486", "A001487", "A001488", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M4618", "N1971" ]
N. J. A. Sloane
2023-09-05T01:20:41
oeisdata/seq/A001/A001487.seq
e4f12d8c963d8c3f5b4dd04944863309
A001488
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^10 in powers of x.
[ "1", "-10", "45", "-120", "200", "-162", "-160", "810", "-1530", "1730", "-749", "-1630", "4755", "-7070", "6700", "-2450", "-5295", "14070", "-20010", "19350", "-10157", "-6290", "25515", "-40660", "44940", "-34268", "9180", "24510", "-57195", "78060", "-79087", "56610", "-13935", "-39600", "89805", "-121638", "125405" ]
[ "sign" ]
26
0
5
[ "A001482", "A001487", "A001488", "A001490", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M4703", "N2010" ]
N. J. A. Sloane
2023-09-05T12:24:33
oeisdata/seq/A001/A001488.seq
447a62874a995051eb11be1d45e4306a
A001489
a(n) = -n.
[ "0", "-1", "-2", "-3", "-4", "-5", "-6", "-7", "-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", "-33", "-34", "-35", "-36", "-37", "-38", "-39", "-40", "-41", "-42", "-43", "-44", "-45", "-46", "-47", "-48", "-49", "-50", "-51", "-52", "-53", "-54", "-55", "-56", "-57", "-58", "-59", "-60", "-61", "-62", "-63", "-64", "-65" ]
[ "core", "sign", "easy" ]
69
0
5
[ "A001489", "A057428" ]
null
N. J. A. Sloane
2022-11-15T01:18:03
oeisdata/seq/A001/A001489.seq
63d8bc5bf33951804b6e40dd98ac744f
A001490
Expansion of {Product_{j>=1} (1 - (-x)^j) - 1}^12 in powers of x.
[ "1", "-12", "66", "-220", "483", "-660", "252", "1320", "-4059", "6644", "-6336", "240", "12255", "-27192", "35850", "-27972", "-2343", "50568", "-99286", "122496", "-96162", "11584", "115116", "-242616", "315216", "-283800", "128304", "126280", "-409398", "622644", "-671550", "501468", "-122508", "-382360" ]
[ "sign" ]
21
0
5
[ "A001482", "A001488", "A001490", "A047638", "A047649", "A047654", "A047655", "A341243" ]
[ "M4845", "N2071" ]
N. J. A. Sloane
2023-09-06T01:31:08
oeisdata/seq/A001/A001490.seq
0bcbcb8a5159cc18906ab01a076e3381
A001491
Opus numbers of Beethoven's nine symphonies.
[ "21", "36", "55", "60", "67", "68", "92", "93", "125" ]
[ "fini", "full", "nonn" ]
14
0
5
null
null
N. J. A. Sloane, GEIER(AT)LaDune.Westfalen.De (Michael Gierhake)
2022-06-04T09:50:48
oeisdata/seq/A001/A001491.seq
d26df24ef937597f557563f7e051bd9e
A001492
Clock chimes with a quarter-hour bell.
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "4", "1", "1", "1", "5", "1", "1", "1", "6", "1", "1", "1", "7", "1", "1", "1", "8", "1", "1", "1", "9", "1", "1", "1", "10", "1", "1", "1", "11", "1", "1", "1", "12", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "4", "1", "1", "1", "5", "1", "1", "1", "6", "1", "1", "1", "7", "1", "1", "1", "8", "1", "1", "1", "9" ]
[ "nonn", "easy" ]
19
0
5
[ "A001492", "A007879", "A007884" ]
null
N. J. A. Sloane
2020-08-16T01:47:46
oeisdata/seq/A001/A001492.seq
d4a90a80842e92155deff1e6b0dccc25
A001493
Erroneous version of A000637.
[ "1", "1", "1", "2", "7", "8", "37", "40", "200", "258", "1039", "1500" ]
[ "dead" ]
9
0
5
null
null
null
2010-07-31T03:00:00
oeisdata/seq/A001/A001493.seq
580cdfd1a24ae7e88c207418b780fa70
A001494
Numbers k such that phi(k) = phi(k+2).
[ "4", "7", "8", "10", "26", "32", "70", "74", "122", "146", "308", "314", "386", "512", "554", "572", "626", "635", "728", "794", "842", "910", "914", "1015", "1082", "1226", "1322", "1330", "1346", "1466", "1514", "1608", "1754", "1994", "2132", "2170", "2186", "2306", "2402", "2426", "2474", "2590", "2642", "2695", "2762", "2906", "3242", "3314" ]
[ "nonn", "nice" ]
98
0
5
[ "A000010", "A001274", "A001494", "A007015", "A179186", "A179187", "A179188", "A179189", "A179202", "A217139" ]
[ "M3293", "N1328" ]
N. J. A. Sloane
2024-02-16T01:20:07
oeisdata/seq/A001/A001494.seq
b56c418078b853c6bac2ccbd2f201632
A001495
Number of symmetric 0-1 (n+1) X (n+1) matrices with row sums 2 and first row starting 1,1 for n > 0, a(0)=1.
[ "1", "1", "1", "3", "13", "70", "462", "3592", "32056", "322626", "3611890", "44491654", "597714474", "8693651092", "136059119332", "2279212812480", "40681707637888", "770631412413148", "15438647456063004", "326091322648369684", "7241563996136849260", "168657537987709667976", "4110364564664358194536" ]
[ "nonn" ]
54
0
5
null
[ "M2947", "N1188" ]
N. J. A. Sloane
2024-12-27T00:44:47
oeisdata/seq/A001/A001495.seq
f917db07eddcd8bed638ce4fb671d50b
A001496
Number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to n.
[ "1", "24", "282", "2008", "10147", "40176", "132724", "381424", "981541", "2309384", "5045326", "10356424", "20158151", "37478624", "66952936", "115479776", "193077449", "313981688", "498033282", "772409528", "1173759851", "1750812624", "2567527260", "3706873040" ]
[ "nonn", "easy", "nice" ]
61
0
5
[ "A001496", "A002721", "A002817", "A003438", "A019298", "A257493" ]
[ "M5158", "N2240" ]
N. J. A. Sloane
2019-01-23T12:36:25
oeisdata/seq/A001/A001496.seq
6e5486a628cac45a09c21b332de2c980
A001497
Triangle of coefficients of Bessel polynomials (exponents in decreasing order).
[ "1", "1", "1", "3", "3", "1", "15", "15", "6", "1", "105", "105", "45", "10", "1", "945", "945", "420", "105", "15", "1", "10395", "10395", "4725", "1260", "210", "21", "1", "135135", "135135", "62370", "17325", "3150", "378", "28", "1", "2027025", "2027025", "945945", "270270", "51975", "6930", "630", "36", "1", "34459425", "34459425", "16216200", "4729725", "945945", "135135", "13860", "990", "45", "1" ]
[ "nonn", "tabl", "nice" ]
187
0
5
[ "A001147", "A001497", "A001498", "A001515", "A039683", "A054142", "A099174", "A100861", "A104556", "A107102", "A111924", "A122850", "A144299", "A245066" ]
null
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001497.seq
8974ca5bfbf5a207b5117341db7a5c02
A001498
Triangle a(n,k) (n >= 0, 0 <= k <= n) of coefficients of Bessel polynomials y_n(x) (exponents in increasing order).
[ "1", "1", "1", "1", "3", "3", "1", "6", "15", "15", "1", "10", "45", "105", "105", "1", "15", "105", "420", "945", "945", "1", "21", "210", "1260", "4725", "10395", "10395", "1", "28", "378", "3150", "17325", "62370", "135135", "135135", "1", "36", "630", "6930", "51975", "270270", "945945", "2027025", "2027025", "1", "45", "990", "13860", "135135", "945945", "4729725", "16216200", "34459425", "34459425" ]
[ "nonn", "tabl", "nice", "easy" ]
168
0
5
[ "A000217", "A000457", "A000806", "A001147", "A001497", "A001498", "A001515", "A001517", "A001518", "A001879", "A001880", "A001881", "A002119", "A003215", "A038121", "A043301", "A050534", "A065919", "A065923", "A100861", "A111924", "A113025", "A144299", "A144331", "A245066" ]
null
N. J. A. Sloane
2025-03-31T04:50:03
oeisdata/seq/A001/A001498.seq
140c8acbdb19fd7570c131c0e62b5193
A001499
Number of n X n matrices with exactly 2 1's in each row and column, other entries 0.
[ "1", "0", "1", "6", "90", "2040", "67950", "3110940", "187530840", "14398171200", "1371785398200", "158815387962000", "21959547410077200", "3574340599104475200", "676508133623135814000", "147320988741542099484000", "36574751938491748341360000", "10268902998771351157327104000" ]
[ "nonn", "nice", "easy" ]
113
0
5
[ "A000290", "A000681", "A000986", "A001499", "A001501", "A002411", "A005408", "A007107", "A008300", "A053871", "A123544", "A284989" ]
[ "M4286", "N1792" ]
N. J. A. Sloane
2025-01-26T02:45:01
oeisdata/seq/A001/A001499.seq
44f1059c9d5561b7c191983f5c306f05
A001500
Number of stochastic matrices of integers: n X n arrays of nonnegative integers with all row and column sums equal to 3.
[ "1", "1", "4", "55", "2008", "153040", "20933840", "4662857360", "1579060246400", "772200774683520", "523853880779443200", "477360556805016931200", "569060910292172349004800", "868071731152923490921728000", "1663043727673392444887284377600", "3937477620391471128913917360384000" ]
[ "nonn", "easy" ]
76
0
5
[ "A000681", "A001500", "A246970", "A257493", "A269743", "A344379" ]
[ "M3689", "N1507" ]
N. J. A. Sloane
2021-05-17T04:17:56
oeisdata/seq/A001/A001500.seq
3e277e8482ba32b914eceb27eed77c5b