Datasets:
christopher
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oeis

Dataset card Data Studio Files
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1999-12-11 03:00:00
2025-04-25 01:21:50
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32
A001501
Number of n X n 0-1 matrices with all column and row sums equal to 3.
[ "1", "0", "0", "1", "24", "2040", "297200", "68938800", "24046189440", "12025780892160", "8302816499443200", "7673688777463632000", "9254768770160124288000", "14255616537578735986867200", "27537152449960680597739468800", "65662040698002721810659005184000" ]
[ "nonn", "nice" ]
78
0
5
[ "A001499", "A001501", "A008300", "A284990" ]
[ "M5175", "N2247" ]
N. J. A. Sloane
2023-10-27T19:26:21
oeisdata/seq/A001/A001501.seq
d322dbad3018e704ddc21d8976d52290
A001502
Largest number requiring n syllables in English (U.S.) - not well-defined, but the next term may be twelve millillion, too large to write down here.
[ "12", "90", "12000000000000" ]
[ "word", "nonn", "bref" ]
8
0
5
null
null
N. J. A. Sloane
2022-02-01T23:42:02
oeisdata/seq/A001/A001502.seq
fa91ca63c3570df7136d6c6a3db417d0
A001503
Largest number requiring n syllables in English (U.K.) - not well-defined, but the next term may be twelve millillion, too large to write down here.
[ "12", "90", "12000000000000000000" ]
[ "word", "nonn", "bref" ]
8
0
5
null
null
N. J. A. Sloane
2022-02-01T23:42:17
oeisdata/seq/A001/A001503.seq
3e76e68bed18c5608d9aff9b5ec75f14
A001504
a(n) = (3*n+1)*(3*n+2).
[ "2", "20", "56", "110", "182", "272", "380", "506", "650", "812", "992", "1190", "1406", "1640", "1892", "2162", "2450", "2756", "3080", "3422", "3782", "4160", "4556", "4970", "5402", "5852", "6320", "6806", "7310", "7832", "8372", "8930", "9506", "10100", "10712", "11342", "11990", "12656", "13340", "14042", "14762", "15500", "16256", "17030" ]
[ "nonn", "easy" ]
82
0
5
[ "A001504", "A002378", "A016777", "A016789", "A060544", "A073010" ]
null
N. J. A. Sloane
2025-03-16T13:16:33
oeisdata/seq/A001/A001504.seq
b1bab9c219b3435852becc49a06c1654
A001505
a(n) = (4n+1)(4n+2)(4n+3).
[ "6", "210", "990", "2730", "5814", "10626", "17550", "26970", "39270", "54834", "74046", "97290", "124950", "157410", "195054", "238266", "287430", "342930", "405150", "474474", "551286", "635970", "728910", "830490", "941094", "1061106", "1190910", "1330890", "1481430", "1642914", "1815726", "2000250", "2196870", "2405970" ]
[ "nonn", "easy" ]
47
0
5
[ "A001505", "A015219" ]
null
N. J. A. Sloane
2024-04-17T10:55:53
oeisdata/seq/A001/A001505.seq
51c0ff9f85f230559864f331bc7c5c07
A001506
a(n) is the number of c-nets with n+1 vertices and 2n edges, n >= 1.
[ "0", "0", "1", "4", "24", "188", "1705", "16980", "180670", "2020120", "23478426", "281481880", "3461873536", "43494961404", "556461656569", "7230987646484", "95244774132810", "1269534571172912", "17100621281619328", "232511930087682528", "3188042426888493288" ]
[ "nonn" ]
40
0
5
[ "A001506", "A290326" ]
[ "M3603", "N1462" ]
N. J. A. Sloane
2017-07-28T09:38:40
oeisdata/seq/A001/A001506.seq
a3a72a9204da6798479755f16b54c737
A001507
a(n) is the number of c-nets with n+1 vertices and 2n+1 edges, n >= 1.
[ "0", "0", "0", "3", "33", "338", "3580", "39525", "452865", "5354832", "65022840", "807560625", "10224817515", "131631305718", "1719292293940", "22743461653913", "304256251541865", "4111134671255120", "56049154766899216", "770325744569310630", "10664613057653024586", "148625522045319923940" ]
[ "nonn" ]
39
0
5
[ "A001507", "A290326" ]
[ "M3132", "N1270" ]
N. J. A. Sloane
2017-07-28T09:38:08
oeisdata/seq/A001/A001507.seq
9a11887c875f2ebf109d20b19a8f6a61
A001508
a(n) is the number of c-nets with n+1 vertices and 2n+2 edges, n >= 1.
[ "0", "0", "0", "0", "13", "252", "3740", "51300", "685419", "9095856", "120872850", "1614234960", "21697730835", "293695935764", "4003423965684", "54944523689692", "758990230992175", "10548884795729280", "147458773053913268", "2072369440050644208", "29271357456284966994" ]
[ "nonn" ]
37
0
5
[ "A001508", "A290326" ]
[ "M4918", "N2111" ]
N. J. A. Sloane
2017-07-28T09:38:50
oeisdata/seq/A001/A001508.seq
5d34ba371aceecf02bb3ac2adb77c4b9
A001509
a(n) = (5*n + 1)*(5*n + 2)*(5*n + 3).
[ "6", "336", "1716", "4896", "10626", "19656", "32736", "50616", "74046", "103776", "140556", "185136", "238266", "300696", "373176", "456456", "551286", "658416", "778596", "912576", "1061106", "1224936", "1404816", "1601496", "1815726", "2048256", "2299836", "2571216", "2863146", "3176376", "3511656", "3869736", "4251366" ]
[ "nonn", "easy" ]
31
0
5
[ "A001509", "A001622", "A016861", "A016873", "A016885" ]
null
N. J. A. Sloane, Dec 11 1996
2023-01-26T10:10:16
oeisdata/seq/A001/A001509.seq
f4750c0f2a4630cfb97d290fd4d91499
A001510
a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1, with a(0) = 1, a(1) = 2.
[ "1", "2", "4", "24", "1104", "2435424", "11862575248704", "281441383062305809756861824", "158418504200047111075388369241884118003210485743490304" ]
[ "nonn", "nice" ]
37
0
5
[ "A001510", "A001622", "A002715" ]
[ "M1301", "N0499" ]
N. J. A. Sloane
2025-01-09T08:18:26
oeisdata/seq/A001/A001510.seq
b196c3405646976adbd402164fefad34
A001511
The ruler function: exponent of the highest power of 2 dividing 2n. Equivalently, the 2-adic valuation of 2n.
[ "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "5", "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "6", "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "5", "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "7", "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "5", "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "6", "1", "2", "1", "3", "1", "2", "1", "4", "1" ]
[ "mult", "nonn", "nice", "easy", "core", "hear" ]
563
0
5
[ "A000005", "A000041", "A000079", "A001511", "A002487", "A003188", "A003278", "A003602", "A005187", "A007814", "A007949", "A018238", "A035263", "A047999", "A050600", "A050603", "A050604", "A051064", "A051731", "A054525", "A054852", "A055457", "A065176", "A067029", "A082850", "A085058", "A089080", "A089309", "A092119", "A092673", "A112302", "A115362", "A117303", "A129360", "A130093", "A135416", "A171977", "A173238", "A181988", "A209229", "A220466", "A287896" ]
[ "M0127", "N0051" ]
N. J. A. Sloane
2025-02-16T08:32:23
oeisdata/seq/A001/A001511.seq
58d6596f55b7350529f88770bcaefd7d
A001512
a(n) = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4).
[ "24", "3024", "24024", "93024", "255024", "570024", "1113024", "1974024", "3258024", "5085024", "7590024", "10923024", "15249024", "20748024", "27615024", "36060024", "46308024", "58599024", "73188024", "90345024", "110355024", "133518024", "160149024", "190578024", "225150024", "264225024", "308178024" ]
[ "nonn", "easy" ]
29
0
5
[ "A001512", "A001622", "A151989" ]
null
N. J. A. Sloane
2022-10-21T21:11:20
oeisdata/seq/A001/A001512.seq
21417651d7e88e87a64ad36ec5d3039c
A001513
a(n) = (6*n+1)*(6*n+5).
[ "5", "77", "221", "437", "725", "1085", "1517", "2021", "2597", "3245", "3965", "4757", "5621", "6557", "7565", "8645", "9797", "11021", "12317", "13685", "15125", "16637", "18221", "19877", "21605", "23405", "25277", "27221", "29237", "31325", "33485", "35717", "38021", "40397", "42845", "45365", "47957", "50621", "53357", "56165", "59045" ]
[ "nonn", "easy" ]
32
0
5
[ "A001513", "A016921", "A016969" ]
null
N. J. A. Sloane
2023-02-19T03:33:24
oeisdata/seq/A001/A001513.seq
9cb012628fe319996c769360498f0443
A001514
Bessel polynomial {y_n}'(1).
[ "0", "1", "9", "81", "835", "9990", "137466", "2148139", "37662381", "733015845", "15693217705", "366695853876", "9289111077324", "253623142901401", "7425873460633005", "232122372003909045", "7715943399320562331", "271796943164015920914", "10114041937573463433966" ]
[ "nonn" ]
37
0
5
[ "A001514", "A001515", "A001516", "A001518", "A065920", "A144505" ]
[ "M4654", "N1993" ]
N. J. A. Sloane
2020-02-16T10:51:08
oeisdata/seq/A001/A001514.seq
db341dd94bed26c3203f25dc123f18e9
A001515
Bessel polynomial y_n(x) evaluated at x=1.
[ "1", "2", "7", "37", "266", "2431", "27007", "353522", "5329837", "90960751", "1733584106", "36496226977", "841146804577", "21065166341402", "569600638022431", "16539483668991901", "513293594376771362", "16955228098102446847", "593946277027962411007", "21992967478132711654106", "858319677924203716921141" ]
[ "nonn", "easy", "nice" ]
155
0
5
[ "A000108", "A000806", "A001497", "A001498", "A001514", "A001515", "A001517", "A105748", "A105749", "A143990", "A144301", "A144416", "A144498", "A144505", "A144506", "A144507", "A144508", "A144509", "A144513", "A144514", "A149187", "A281358", "A281359", "A281360", "A281361" ]
[ "M1803", "N0713" ]
N. J. A. Sloane
2025-02-25T10:35:53
oeisdata/seq/A001/A001515.seq
dd050dbae6dd0f0417948072bf3cf0d5
A001516
Bessel polynomial {y_n}''(1).
[ "0", "0", "6", "120", "1980", "32970", "584430", "11204676", "233098740", "5254404210", "127921380840", "3350718545460", "94062457204716", "2819367702529560", "89912640142178490", "3040986592542420060", "108752084073199561140", "4101112025363285051526" ]
[ "nonn", "easy" ]
39
0
5
[ "A001497", "A001498", "A001514", "A001515", "A001516", "A001518", "A065944", "A144505" ]
[ "M4295", "N1795" ]
N. J. A. Sloane
2020-02-16T10:51:19
oeisdata/seq/A001/A001516.seq
c1694622588cd6eda40f113ce8ebbe77
A001517
Bessel polynomials y_n(x) (see A001498) evaluated at 2.
[ "1", "3", "19", "193", "2721", "49171", "1084483", "28245729", "848456353", "28875761731", "1098127402131", "46150226651233", "2124008553358849", "106246577894593683", "5739439214861417731", "332993721039856822081", "20651350143685984386753" ]
[ "nonn", "easy", "nice" ]
111
0
5
[ "A001515", "A001517", "A001518", "A002119", "A053556", "A053557", "A080893", "A099022", "A105747", "A243593" ]
[ "M3062", "N1240" ]
N. J. A. Sloane
2023-10-27T19:35:43
oeisdata/seq/A001/A001517.seq
dcab6bf22704e2d6d24960af1886a904
A001518
Bessel polynomial y_n(3).
[ "1", "4", "37", "559", "11776", "318511", "10522639", "410701432", "18492087079", "943507142461", "53798399207356", "3390242657205889", "233980541746413697", "17551930873638233164", "1421940381306443299981", "123726365104534205331511", "11507973895102987539130504" ]
[ "nonn", "easy" ]
80
0
5
[ "A001498", "A001515", "A001517", "A001518" ]
[ "M3669", "N1495" ]
N. J. A. Sloane
2020-02-16T10:51:38
oeisdata/seq/A001/A001518.seq
6d4e0ef5436ff78469c4cc5cf2a6ed4a
A001519
a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1.
[ "1", "1", "2", "5", "13", "34", "89", "233", "610", "1597", "4181", "10946", "28657", "75025", "196418", "514229", "1346269", "3524578", "9227465", "24157817", "63245986", "165580141", "433494437", "1134903170", "2971215073", "7778742049", "20365011074", "53316291173", "139583862445", "365435296162", "956722026041" ]
[ "nonn", "nice", "easy", "core" ]
845
0
5
[ "A000045", "A001519", "A001622", "A001653", "A001654", "A001906", "A002559", "A055105", "A055106", "A055107", "A060920", "A074664", "A082582", "A094954", "A101368", "A104457", "A122367", "A124292", "A124293", "A124294", "A124295", "A130255", "A130256", "A140068", "A140069", "A144257", "A152251", "A153266", "A153267", "A153342", "A153387", "A153463", "A179745", "A179806", "A211216", "A213948", "A322602" ]
[ "M1439", "N0569" ]
N. J. A. Sloane
2025-03-15T16:34:33
oeisdata/seq/A001/A001519.seq
9e3365cbeb43adf6688449ef71bdfa60
A001520
a(n) = (6*n+1)*(6*n+3)*(6*n+5).
[ "15", "693", "3315", "9177", "19575", "35805", "59163", "90945", "132447", "184965", "249795", "328233", "421575", "531117", "658155", "803985", "969903", "1157205", "1367187", "1601145", "1860375", "2146173", "2459835", "2802657", "3175935", "3580965", "4019043", "4491465", "4999527", "5544525", "6127755", "6750513" ]
[ "nonn", "easy" ]
25
0
5
null
null
N. J. A. Sloane
2022-10-18T15:25:18
oeisdata/seq/A001/A001520.seq
2786ed71c510a6c95ea85d49fb8d27c1
A001521
a(1) = 1; thereafter a(n+1) = floor(sqrt(2*a(n)*(a(n)+1))).
[ "1", "2", "3", "4", "6", "9", "13", "19", "27", "38", "54", "77", "109", "154", "218", "309", "437", "618", "874", "1236", "1748", "2472", "3496", "4944", "6992", "9888", "13984", "19777", "27969", "39554", "55938", "79108", "111876", "158217", "223753", "316435", "447507", "632871", "895015", "1265743", "1790031", "2531486", "3580062", "5062972" ]
[ "nonn", "nice", "easy", "changed" ]
98
0
5
[ "A000196", "A001521", "A017911", "A190660", "A241576" ]
[ "M0569", "N0206" ]
N. J. A. Sloane
2025-04-20T03:46:08
oeisdata/seq/A001/A001521.seq
efd483a9dc00c631fd242c8b70a0603d
A001522
Number of n-stacks with strictly receding walls, or the number of Type A partitions of n in the sense of Auluck (1951).
[ "1", "1", "1", "1", "2", "3", "5", "7", "10", "14", "19", "26", "35", "47", "62", "82", "107", "139", "179", "230", "293", "372", "470", "591", "740", "924", "1148", "1422", "1756", "2161", "2651", "3244", "3957", "4815", "5844", "7075", "8545", "10299", "12383", "14859", "17794", "21267", "25368", "30207", "35902", "42600", "50462", "59678", "70465", "83079", "97800", "114967", "134956", "158205", "185209", "216546", "252859" ]
[ "nonn", "easy", "nice" ]
135
0
5
[ "A000041", "A000166", "A000700", "A001522", "A001523", "A001524", "A002467", "A003242", "A008292", "A059776", "A064391", "A064410", "A064428", "A088902", "A114088", "A114921", "A115720", "A115994", "A118199", "A238351", "A238352", "A238394", "A238395", "A257989", "A325187", "A342192", "A342527", "A342528", "A342532", "A352822", "A352827", "A352828", "A352829", "A352830", "A352832", "A352833", "A352872", "A352873", "A352874" ]
[ "M0644", "N0238" ]
N. J. A. Sloane
2024-12-27T00:44:40
oeisdata/seq/A001/A001522.seq
af61a5bb74ff123cbb4c106af75a84fe
A001523
Number of stacks, or planar partitions of n; also weakly unimodal compositions of n.
[ "1", "1", "2", "4", "8", "15", "27", "47", "79", "130", "209", "330", "512", "784", "1183", "1765", "2604", "3804", "5504", "7898", "11240", "15880", "22277", "31048", "43003", "59220", "81098", "110484", "149769", "202070", "271404", "362974", "483439", "641368", "847681", "1116325", "1464999", "1916184", "2498258", "3247088", "4207764" ]
[ "nonn", "nice", "easy" ]
129
0
5
[ "A000569", "A001522", "A001523", "A001524", "A007052", "A054250", "A059204", "A059618", "A059623", "A072704", "A072706", "A100505", "A100506", "A107429", "A115981", "A156253", "A227038", "A247255", "A328509", "A329398", "A332280", "A332282", "A332283", "A332285", "A332288", "A332294", "A332577", "A332578", "A332642", "A332669", "A332726" ]
[ "M1102", "N0420" ]
N. J. A. Sloane
2025-03-31T04:50:08
oeisdata/seq/A001/A001523.seq
215c8c2995b1f3e2a43e102f65109b6a
A001524
Number of stacks, or arrangements of n pennies in contiguous rows, each touching 2 in row below.
[ "1", "1", "1", "2", "3", "5", "8", "12", "18", "26", "38", "53", "75", "103", "142", "192", "260", "346", "461", "607", "797", "1038", "1348", "1738", "2234", "2856", "3638", "4614", "5832", "7342", "9214", "11525", "14369", "17863", "22142", "27371", "33744", "41498", "50903", "62299", "76066", "92676", "112666", "136696", "165507", "200018" ]
[ "nonn", "nice", "easy" ]
95
0
5
[ "A001522", "A001523", "A001524", "A007293", "A015128", "A171604", "A259095" ]
[ "M0687", "N0253" ]
N. J. A. Sloane
2021-06-06T05:49:39
oeisdata/seq/A001/A001524.seq
e6cbe6fb8cb4bf29a3eae777cc8cbea1
A001525
a(n) = (3n)!/(3!n!).
[ "1", "60", "10080", "3326400", "1816214400", "1482030950400", "1689515283456000", "2564684200286208000", "5001134190558105600000", "12182762888199545241600000", "36255902355281846639001600000", "129433571408356192501235712000000", "545950804200446419970212233216000000" ]
[ "nonn" ]
25
0
5
[ "A001525", "A064350", "A157704", "A157705" ]
[ "M5320" ]
N. J. A. Sloane
2022-02-02T04:00:45
oeisdata/seq/A001/A001525.seq
3dbd0559d8cb3fe4087b0cad86e0c5f7
A001526
a(n) = (7*n+1)*(7*n+6).
[ "6", "104", "300", "594", "986", "1476", "2064", "2750", "3534", "4416", "5396", "6474", "7650", "8924", "10296", "11766", "13334", "15000", "16764", "18626", "20586", "22644", "24800", "27054", "29406", "31856", "34404", "37050", "39794", "42636", "45576", "48614", "51750", "54984", "58316", "61746", "65274", "68900", "72624", "76446" ]
[ "nonn", "easy" ]
32
0
5
[ "A001526", "A016993", "A017053" ]
null
N. J. A. Sloane
2024-10-25T07:44:48
oeisdata/seq/A001/A001526.seq
0218aaefc306c0a870b7bf4d84dbc503
A001527
a(n) = 2 * Sum_{i=0..n} C(2^n-1, i).
[ "2", "4", "14", "128", "3882", "412736", "151223522", "189581406208", "820064805806914", "12419746847290729472", "668590083306794321516802", "129667782549203712117025325056", "91624448643446654575608517356620802", "238057970008583161105667221977375792447488" ]
[ "nonn", "easy" ]
17
0
5
[ "A001527", "A046855" ]
[ "M1286", "N0493" ]
N. J. A. Sloane
2020-04-26T22:53:38
oeisdata/seq/A001/A001527.seq
c0e2fcf2c658217448f8d5b62d239196
A001528
NPN-equivalence classes of switching functions of exactly n variables.
[ "1", "1", "2", "10", "208", "615904", "200253951911058" ]
[ "nonn", "more" ]
32
0
5
null
[ "M1991", "N0785" ]
N. J. A. Sloane
2022-02-01T23:44:36
oeisdata/seq/A001/A001528.seq
34d0bc30e62009cd486e581ab0ee7f82
A001529
NPN-equivalence classes of threshold functions of n or fewer variables.
[ "1", "2", "3", "6", "15", "63", "567", "14755", "1366318" ]
[ "nonn", "nice", "more" ]
20
0
5
[ "A001529", "A001530", "A002078", "A002079" ]
[ "M0809", "N0306" ]
N. J. A. Sloane.
2015-07-28T12:27:42
oeisdata/seq/A001/A001529.seq
2e30ae7c5b9560748538a1caddb9a015
A001530
NPN-equivalence classes of threshold functions of exactly n variables.
[ "1", "1", "1", "3", "9", "48", "504", "14188", "1351563" ]
[ "nonn", "more" ]
24
0
5
[ "A001529", "A001530" ]
[ "M2825", "N1138" ]
N. J. A. Sloane
2022-02-01T23:45:00
oeisdata/seq/A001/A001530.seq
0f3f5fa4ea71c359f2b46236aa0f07fd
A001531
Number of self-dual Boolean functions of n variables that are distinct under complementation/permutation.
[ "1", "1", "3", "7", "83", "109950", "28613442061634", "32966964611113760521683249750048", "623226477875973310927522916529663444655632673539934117923988862064800" ]
[ "nonn", "nice" ]
30
0
5
[ "A000610", "A000616", "A001531" ]
[ "M2706", "N1085" ]
N. J. A. Sloane.
2015-07-28T12:05:44
oeisdata/seq/A001/A001531.seq
fbc3f4521c11b400d7429bb1fd222789
A001532
Number of NP-equivalence classes of self-dual threshold functions of n or fewer variables ; number of majority (i.e., decisive and weighted) games with n players.
[ "1", "1", "2", "3", "7", "21", "135", "2470", "175428", "52980624" ]
[ "nonn", "nice", "more" ]
74
0
5
[ "A000617", "A001532", "A002077", "A002080", "A003184", "A109456", "A132183", "A189359" ]
[ "M0852", "N0324" ]
N. J. A. Sloane
2023-10-27T09:59:50
oeisdata/seq/A001/A001532.seq
24677135f456bef2de957c9d8a571f72
A001533
a(n) = (8*n+1)*(8*n+7).
[ "7", "135", "391", "775", "1287", "1927", "2695", "3591", "4615", "5767", "7047", "8455", "9991", "11655", "13447", "15367", "17415", "19591", "21895", "24327", "26887", "29575", "32391", "35335", "38407", "41607", "44935", "48391", "51975", "55687", "59527", "63495", "67591", "71815", "76167", "80647", "85255", "89991", "94855", "99847", "104967" ]
[ "nonn", "easy" ]
55
0
5
[ "A001533", "A001539", "A004771", "A017077", "A017113", "A028560", "A250129" ]
null
N. J. A. Sloane
2024-10-25T07:40:35
oeisdata/seq/A001/A001533.seq
9eb4a3c1b783b93374c5b41989b924bb
A001534
a(n) = (9*n+1)*(9*n+8).
[ "8", "170", "494", "980", "1628", "2438", "3410", "4544", "5840", "7298", "8918", "10700", "12644", "14750", "17018", "19448", "22040", "24794", "27710", "30788", "34028", "37430", "40994", "44720", "48608", "52658", "56870", "61244", "65780", "70478", "75338", "80360", "85544", "90890", "96398", "102068", "107900", "113894", "120050" ]
[ "nonn", "easy" ]
43
0
5
[ "A001534", "A017173", "A017257" ]
null
N. J. A. Sloane
2024-10-18T19:39:38
oeisdata/seq/A001/A001534.seq
f3f9c55320351f98e5241f24f654f402
A001535
a(n) = (10n+1)*(10n+9).
[ "9", "209", "609", "1209", "2009", "3009", "4209", "5609", "7209", "9009", "11009", "13209", "15609", "18209", "21009", "24009", "27209", "30609", "34209", "38009", "42009", "46209", "50609", "55209", "60009", "65009", "70209", "75609", "81209", "87009", "93009", "99209", "105609", "112209", "119009", "126009", "133209", "140609" ]
[ "nonn", "easy" ]
28
0
5
[ "A001535", "A001622", "A017281", "A017377" ]
null
N. J. A. Sloane
2023-02-20T03:14:37
oeisdata/seq/A001/A001535.seq
4d14047cdceeb80f915e1a21dea607f0
A001536
a(n) = (11*n+1)*(11*n+10).
[ "10", "252", "736", "1462", "2430", "3640", "5092", "6786", "8722", "10900", "13320", "15982", "18886", "22032", "25420", "29050", "32922", "37036", "41392", "45990", "50830", "55912", "61236", "66802", "72610", "78660", "84952", "91486", "98262", "105280", "112540", "120042", "127786", "135772", "144000", "152470", "161182", "170136" ]
[ "nonn", "easy" ]
29
0
5
[ "A001536", "A017401", "A017509" ]
null
N. J. A. Sloane
2024-10-25T08:25:59
oeisdata/seq/A001/A001536.seq
c3de432758887c421d473b8c6e888294
A001537
Invertible Boolean functions with AG(n,2) acting on the domain and range.
[ "1", "1", "4", "302", "2569966041123963092", "76230976900860740792605252293646252383143627390965685153124757864" ]
[ "nonn" ]
29
0
5
null
[ "M3723", "N1522" ]
N. J. A. Sloane
2022-02-02T04:51:56
oeisdata/seq/A001/A001537.seq
86ce5c7f2865a53ad35f00e049d3b808
A001538
a(n) = (12*n+1)*(12*n+11).
[ "11", "299", "875", "1739", "2891", "4331", "6059", "8075", "10379", "12971", "15851", "19019", "22475", "26219", "30251", "34571", "39179", "44075", "49259", "54731", "60491", "66539", "72875", "79499", "86411", "93611", "101099", "108875", "116939", "125291", "133931", "142859", "152075", "161579", "171371", "181451", "191819" ]
[ "nonn", "easy" ]
37
0
5
[ "A001533", "A001538", "A017533", "A017653" ]
null
N. J. A. Sloane
2024-10-25T17:05:36
oeisdata/seq/A001/A001538.seq
8870a994d62af31f7a4b31b77f8eda2e
A001539
a(n) = (4*n+1)*(4*n+3).
[ "3", "35", "99", "195", "323", "483", "675", "899", "1155", "1443", "1763", "2115", "2499", "2915", "3363", "3843", "4355", "4899", "5475", "6083", "6723", "7395", "8099", "8835", "9603", "10403", "11235", "12099", "12995", "13923", "14883", "15875", "16899", "17955", "19043", "20163", "21315", "22499", "23715", "24963", "26243", "27555", "28899" ]
[ "nonn", "easy" ]
69
0
5
[ "A000217", "A000290", "A000466", "A001533", "A001538", "A001539", "A004767", "A016286", "A016813", "A016826", "A133766", "A154633", "A157142" ]
null
N. J. A. Sloane
2024-10-23T17:21:15
oeisdata/seq/A001/A001539.seq
fb10528bec92358d779a1e4dddef9135
A001540
Number of transpositions needed to generate permutations of length n.
[ "0", "2", "8", "36", "184", "1110", "7776", "62216", "559952", "5599530", "61594840", "739138092", "9608795208", "134523132926", "2017846993904", "32285551902480", "548854382342176", "9879378882159186", "187708198761024552", "3754163975220491060", "78837443479630312280", "1734423756551866870182" ]
[ "nonn", "easy", "nice" ]
51
0
5
[ "A001540", "A009179" ]
[ "M1856", "N0734" ]
N. J. A. Sloane
2022-09-08T08:44:29
oeisdata/seq/A001/A001540.seq
01b256c88a1857685980f33c57ded7be
A001541
a(0) = 1, a(1) = 3; for n > 1, a(n) = 6*a(n-1) - a(n-2).
[ "1", "3", "17", "99", "577", "3363", "19601", "114243", "665857", "3880899", "22619537", "131836323", "768398401", "4478554083", "26102926097", "152139002499", "886731088897", "5168247530883", "30122754096401", "175568277047523", "1023286908188737", "5964153172084899", "34761632124320657" ]
[ "nonn", "easy", "nice" ]
446
0
5
[ "A001109", "A001333", "A001541", "A001542", "A001601", "A003499", "A005319", "A046090", "A053142", "A055792", "A055997", "A056771", "A077420", "A082532", "A084130", "A132592", "A188645" ]
[ "M3037", "N1231" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001541.seq
04c67f166a449014d82f8a491cc033f8
A001542
a(n) = 6*a(n-1) - a(n-2) for n > 1, a(0)=0 and a(1)=2.
[ "0", "2", "12", "70", "408", "2378", "13860", "80782", "470832", "2744210", "15994428", "93222358", "543339720", "3166815962", "18457556052", "107578520350", "627013566048", "3654502875938", "21300003689580", "124145519261542", "723573111879672" ]
[ "nonn", "easy", "nice" ]
284
0
5
[ "A000129", "A001108", "A001353", "A001541", "A001542", "A001653", "A001835", "A003499", "A007805", "A007913", "A115598", "A125650", "A125651", "A125652" ]
[ "M2030", "N0802" ]
N. J. A. Sloane
2025-01-06T10:57:58
oeisdata/seq/A001/A001542.seq
21abbbaa624dd673967ec81ce5f95a08
A001543
a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0.
[ "1", "6", "11", "71", "4691", "21982031", "483209576974811", "233491495280173380882643611671", "54518278368171228201482876236565907627201914279213829353891" ]
[ "nonn" ]
55
0
5
[ "A001543", "A177888" ]
[ "M4091", "N1699" ]
N. J. A. Sloane.
2025-01-09T08:19:49
oeisdata/seq/A001/A001543.seq
4d973878302a91cf9fe760263c5bab25
A001544
A nonlinear recurrence: a(n) = a(n-1)^2 - 6*a(n-1) + 6, with a(0) = 1, a(1) = 7.
[ "1", "7", "13", "97", "8833", "77968897", "6079148431583233", "36956045653220845240164417232897", "1365749310322943329964576677590044473746108255675592519835615233" ]
[ "nonn" ]
39
0
5
[ "A001544", "A177888" ]
[ "M4346", "N1820" ]
N. J. A. Sloane
2025-01-15T14:06:35
oeisdata/seq/A001/A001544.seq
08f1ca36ad8672255389a10d90b535b2
A001545
a(n) = (5*n+1)*(5*n+4).
[ "4", "54", "154", "304", "504", "754", "1054", "1404", "1804", "2254", "2754", "3304", "3904", "4554", "5254", "6004", "6804", "7654", "8554", "9504", "10504", "11554", "12654", "13804", "15004", "16254", "17554", "18904", "20304", "21754", "23254", "24804", "26404", "28054", "29754", "31504", "33304", "35154", "37054", "39004", "41004", "43054" ]
[ "nonn", "easy" ]
48
0
5
[ "A000217", "A001545", "A001622", "A016861", "A016897", "A177059", "A200135", "A200138" ]
null
N. J. A. Sloane
2024-10-24T15:42:26
oeisdata/seq/A001/A001545.seq
9eb8ecc2d975f7421a2b0a462b8f73e5
A001546
a(n) = (8*n+1)*(8*n+3)*(8*n+5)*(8*n+7).
[ "105", "19305", "156009", "606825", "1666665", "3728745", "7284585", "12924009", "21335145", "33304425", "49716585", "71554665", "99900009", "135932265", "180929385", "236267625", "303421545", "383964009", "479566185", "591997545", "723125865", "874917225", "1049436009", "1248844905", "1475404905" ]
[ "nonn", "easy" ]
37
0
5
null
null
N. J. A. Sloane
2022-09-08T08:44:29
oeisdata/seq/A001/A001546.seq
e7164bc8a05f36bb2df6feeb8553bfbc
A001547
a(n) = (7*n+1)*(7*n+2)*(7*n+4).
[ "8", "792", "4320", "12650", "27840", "51948", "87032", "135150", "198360", "278720", "378288", "499122", "643280", "812820", "1009800", "1236278", "1494312", "1785960", "2113280", "2478330", "2883168", "3329852", "3820440", "4356990", "4941560", "5576208", "6262992", "7003970", "7801200", "8656740", "9572648" ]
[ "nonn", "easy" ]
23
0
5
null
null
N. J. A. Sloane
2025-02-27T13:05:52
oeisdata/seq/A001/A001547.seq
ad2e05a89759be848876b6106d7efa7d
A001548
Number of connected linear spaces with n (unlabeled) points.
[ "1", "1", "0", "1", "1", "2", "4", "13", "42", "308", "4845", "227613", "28639650" ]
[ "nonn", "hard", "nice", "more" ]
41
0
5
[ "A001200", "A001548", "A056642" ]
[ "M1270", "N0489" ]
N. J. A. Sloane
2024-09-22T07:23:56
oeisdata/seq/A001/A001548.seq
d5406ccb70ed6494a3568eccb2da25a2
A001549
Related to Gilbreath conjecture.
[ "4", "10", "17", "18", "30", "34", "69", "109", "111", "189", "192", "193", "194", "195", "311", "763", "898", "900", "2215", "2810", "2811", "2812", "2813", "3417", "4260", "6000", "6002", "6003", "6004", "23331", "31569", "31601", "31602", "31605", "31606", "31617", "31625", "31627", "92716", "104071", "141818", "141819", "271743", "271747", "325218" ]
[ "nonn" ]
23
0
5
[ "A000232", "A001549", "A036277" ]
[ "M3376", "N1360" ]
N. J. A. Sloane
2023-05-10T10:02:02
oeisdata/seq/A001/A001549.seq
cc87b5c5696b935c8ece7605fe29e2c2
A001550
a(n) = 1^n + 2^n + 3^n.
[ "3", "6", "14", "36", "98", "276", "794", "2316", "6818", "20196", "60074", "179196", "535538", "1602516", "4799354", "14381676", "43112258", "129271236", "387682634", "1162785756", "3487832978", "10462450356", "31385253914", "94151567436", "282446313698", "847322163876" ]
[ "nonn", "easy", "nice" ]
94
0
5
[ "A000051", "A000079", "A000244", "A001550", "A001576", "A001579", "A007689", "A034472", "A034513", "A074501", "A074580", "A103438" ]
[ "M2580", "N1020" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001550.seq
d7b26c2fb0b930d5eb1353bb2128e198
A001551
a(n) = 1^n + 2^n + 3^n + 4^n.
[ "4", "10", "30", "100", "354", "1300", "4890", "18700", "72354", "282340", "1108650", "4373500", "17312754", "68711380", "273234810", "1088123500", "4338079554", "17309140420", "69107159370", "276040692700", "1102999460754", "4408508961460", "17623571298330", "70462895745100", "281757423024354" ]
[ "nonn", "easy", "changed" ]
61
0
5
[ "A001551", "A103438" ]
[ "M3397", "N1375" ]
N. J. A. Sloane
2025-04-14T06:36:09
oeisdata/seq/A001/A001551.seq
f14b8bbc1f4493474d45b2f10c7b1222
A001552
a(n) = 1^n + 2^n + ... + 5^n.
[ "5", "15", "55", "225", "979", "4425", "20515", "96825", "462979", "2235465", "10874275", "53201625", "261453379", "1289414505", "6376750435", "31605701625", "156925970179", "780248593545", "3883804424995", "19349527020825", "96470431101379", "481245667164585", "2401809362313955", "11991391850823225" ]
[ "nonn", "easy" ]
56
0
5
[ "A001552", "A103438" ]
[ "M3863", "N1584" ]
N. J. A. Sloane
2024-10-26T10:13:56
oeisdata/seq/A001/A001552.seq
21edc64cc9082aa730bd75ceb8c5fefe
A001553
a(n) = 1^n + 2^n + ... + 6^n.
[ "6", "21", "91", "441", "2275", "12201", "67171", "376761", "2142595", "12313161", "71340451", "415998681", "2438235715", "14350108521", "84740914531", "501790686201", "2978035877635", "17706908038281", "105443761093411", "628709267031321", "3752628871164355", "22418196307542441", "134023513204581091" ]
[ "nonn", "easy" ]
53
0
5
[ "A001552", "A001553", "A103438" ]
[ "M4149", "N1723" ]
N. J. A. Sloane
2024-10-26T10:15:02
oeisdata/seq/A001/A001553.seq
2dc004f01b019158e34b9d79a16bf8af
A001554
a(n) = 1^n + 2^n + ... + 7^n.
[ "7", "28", "140", "784", "4676", "29008", "184820", "1200304", "7907396", "52666768", "353815700", "2393325424", "16279522916", "111239118928", "762963987380", "5249352196144", "36210966447236", "250337422025488", "1733857359003860", "12027604452404464", "83544895168776356", "580964060390826448" ]
[ "nonn", "easy" ]
46
0
5
[ "A001554", "A103438", "A196837" ]
[ "M4393", "N1850" ]
N. J. A. Sloane
2024-10-26T10:16:03
oeisdata/seq/A001/A001554.seq
e4fe7b58c816fba4a9adbbe9f2f4a038
A001555
a(n) = 1^n + 2^n + ... + 8^n.
[ "8", "36", "204", "1296", "8772", "61776", "446964", "3297456", "24684612", "186884496", "1427557524", "10983260016", "84998999652", "660994932816", "5161010498484", "40433724284976", "317685943157892", "2502137235710736", "19748255868485844", "156142792528260336", "1236466399775623332" ]
[ "nonn", "easy" ]
51
0
5
[ "A001018", "A001552", "A001554", "A001555", "A103438", "A196837" ]
[ "M4520", "N1914" ]
N. J. A. Sloane
2024-10-26T10:17:36
oeisdata/seq/A001/A001555.seq
a5305fed21c3a93e9e6492477c274d20
A001556
a(n) = 1^n + 2^n + ... + 9^n.
[ "9", "45", "285", "2025", "15333", "120825", "978405", "8080425", "67731333", "574304985", "4914341925", "42364319625", "367428536133", "3202860761145", "28037802953445", "246324856379625", "2170706132009733", "19179318935377305", "169842891165484965", "1506994510201252425" ]
[ "nonn" ]
35
0
5
[ "A001556", "A103438", "A196837" ]
[ "M4627", "N1977" ]
N. J. A. Sloane
2024-10-26T10:18:46
oeisdata/seq/A001/A001556.seq
b4c21bde8383262591d5ba8ca31be723
A001557
a(n) = 1^n + 2^n + ... + 10^n.
[ "10", "55", "385", "3025", "25333", "220825", "1978405", "18080425", "167731333", "1574304985", "14914341925", "142364319625", "1367428536133", "13202860761145", "128037802953445", "1246324856379625", "12170706132009733", "119179318935377305", "1169842891165484965", "11506994510201252425" ]
[ "nonn", "easy" ]
47
0
5
[ "A001557", "A103438", "A196837" ]
[ "M4713", "N2014" ]
N. J. A. Sloane
2024-10-24T15:29:15
oeisdata/seq/A001/A001557.seq
8a0c25e1866209ca53bd1eb201466f56
A001558
Number of hill-free Dyck paths of semilength n+3 and having length of first descent equal to 1 (a hill in a Dyck path is a peak at level 1).
[ "1", "3", "10", "33", "111", "379", "1312", "4596", "16266", "58082", "209010", "757259", "2760123", "10114131", "37239072", "137698584", "511140558", "1904038986", "7115422212", "26668376994", "100221202998", "377570383518", "1425706128480", "5394898197448", "20454676622476" ]
[ "nonn", "easy" ]
66
0
5
[ "A000957", "A001558", "A111301", "A118972", "A118973" ]
[ "M2845", "N1143" ]
N. J. A. Sloane
2022-07-05T03:26:25
oeisdata/seq/A001/A001558.seq
233aad331835cdf466cc1654456950a3
A001559
a(0) = 1, a(1) = 4; thereafter a(n)*(2n + 10) - a(n-1)*(11n + 35) + a(n-2)*(8n + 2) + a(n-3)*(15n + 7) + a(n-4)*(4n - 2) = 0.
[ "1", "4", "15", "54", "193", "690", "2476", "8928", "32358", "117866", "431381", "1585842", "5853849", "21690378", "80650536", "300845232", "1125555054", "4222603968", "15881652606", "59873283372", "226214536506", "856431978324", "3248562071800", "12344168149224", "46984664348488", "179114048943078" ]
[ "nonn" ]
59
0
5
null
[ "M3497", "N1418" ]
N. J. A. Sloane
2024-05-19T14:02:53
oeisdata/seq/A001/A001559.seq
e72a77454333b317cb78d49a69ef6989
A001560
Numbers with an even number of partitions.
[ "2", "8", "9", "10", "11", "15", "19", "21", "22", "25", "26", "27", "28", "30", "31", "34", "40", "42", "45", "46", "47", "50", "55", "57", "58", "59", "62", "64", "65", "66", "70", "74", "75", "78", "79", "80", "84", "86", "94", "96", "97", "98", "100", "101", "103", "106", "108", "109", "110", "112", "113", "116", "117", "120", "122", "124", "125", "126", "128", "129", "130", "131" ]
[ "nonn", "easy" ]
39
0
5
[ "A000041", "A001560", "A052001", "A052002", "A243935" ]
[ "M1823", "N0724" ]
N. J. A. Sloane
2021-12-23T22:56:45
oeisdata/seq/A001/A001560.seq
3c24bb8242c261331eb79673e7acfa9f
A001561
a(n) = (7*n+3)*(7*n+5)*(7*n+6).
[ "90", "1560", "6460", "16848", "34782", "62320", "101520", "154440", "223138", "309672", "416100", "544480", "696870", "875328", "1081912", "1318680", "1587690", "1891000", "2230668", "2608752", "3027310", "3488400", "3994080", "4546408", "5147442", "5799240", "6503860", "7263360", "8079798", "8955232", "9891720" ]
[ "nonn", "easy" ]
18
0
5
null
null
N. J. A. Sloane
2025-03-26T18:45:53
oeisdata/seq/A001/A001561.seq
2d3a4b1d9ba8284eb7552a3f197729aa
A001562
Numbers n such that (10^n + 1)/11 is a prime.
[ "5", "7", "19", "31", "53", "67", "293", "641", "2137", "3011", "268207", "1600787" ]
[ "nonn", "hard", "more" ]
58
0
5
[ "A001562", "A054416", "A309358" ]
[ "M3767", "N1537" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001562.seq
b3732f1b8924524f39432219149ee208
A001563
a(n) = n*n! = (n+1)! - n!.
[ "0", "1", "4", "18", "96", "600", "4320", "35280", "322560", "3265920", "36288000", "439084800", "5748019200", "80951270400", "1220496076800", "19615115520000", "334764638208000", "6046686277632000", "115242726703104000", "2311256907767808000", "48658040163532800000", "1072909785605898240000" ]
[ "nonn", "easy", "nice" ]
229
0
5
[ "A000142", "A001563", "A002024", "A002775", "A047920", "A047922", "A053495", "A055089", "A091363", "A091364", "A094485", "A123513", "A143946", "A163931", "A185105", "A229837", "A239069", "A282466", "A322383", "A322384" ]
[ "M3545", "N1436" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001563.seq
34191fd8a59b635297e6c46b6fceadb9
A001564
2nd differences of factorial numbers.
[ "1", "3", "14", "78", "504", "3720", "30960", "287280", "2943360", "33022080", "402796800", "5308934400", "75203251200", "1139544806400", "18394619443200", "315149522688000", "5711921639424000", "109196040425472000", "2196014181064704000", "46346783255764992000", "1024251745442365440000" ]
[ "nonn", "easy" ]
49
0
5
[ "A000142", "A001563", "A001564", "A002061", "A010027", "A047920", "A306209" ]
[ "M2972", "N1202" ]
N. J. A. Sloane
2022-09-08T08:44:29
oeisdata/seq/A001/A001564.seq
84b10b6203717353be3d907e36617ee1
A001565
3rd differences of factorial numbers.
[ "2", "11", "64", "426", "3216", "27240", "256320", "2656080", "30078720", "369774720", "4906137600", "69894316800", "1064341555200", "17255074636800", "296754903244800", "5396772116736000", "103484118786048000", "2086818140639232000", "44150769074700288000", "977904962186600448000" ]
[ "nonn", "easy" ]
41
0
5
[ "A001565", "A047920", "A180196" ]
[ "M2004", "N0793" ]
N. J. A. Sloane
2025-03-26T19:12:32
oeisdata/seq/A001/A001565.seq
25e61c0c0fdd221c635b4118291c6615
A001566
a(0) = 3; thereafter, a(n) = a(n-1)^2 - 2.
[ "3", "7", "47", "2207", "4870847", "23725150497407", "562882766124611619513723647", "316837008400094222150776738483768236006420971486980607" ]
[ "easy", "nonn", "nice", "changed" ]
207
0
5
[ "A000032", "A000045", "A001566", "A002812", "A003010", "A003423", "A003487", "A050614", "A058635", "A088334", "A094874", "A145274", "A145502", "A181393", "A181419", "A186750", "A186751", "A338304" ]
[ "M2705", "N1084" ]
N. J. A. Sloane
2025-04-14T09:03:10
oeisdata/seq/A001/A001566.seq
bbe603a65f4e6dfbd5d8621f04bd5973
A001567
Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers.
[ "341", "561", "645", "1105", "1387", "1729", "1905", "2047", "2465", "2701", "2821", "3277", "4033", "4369", "4371", "4681", "5461", "6601", "7957", "8321", "8481", "8911", "10261", "10585", "11305", "12801", "13741", "13747", "13981", "14491", "15709", "15841", "16705", "18705", "18721", "19951", "23001", "23377", "25761", "29341" ]
[ "nonn", "nice" ]
248
0
5
[ "A001220", "A001567", "A002997", "A005382", "A005935", "A005936", "A005937", "A005938", "A005939", "A020136", "A020137", "A020228", "A052155", "A083737", "A084653", "A153508" ]
[ "M5441", "N2365" ]
N. J. A. Sloane
2025-04-05T10:27:15
oeisdata/seq/A001/A001567.seq
cb9f05664e4a91f2949fbe55c145e86c
A001568
Related to 3-line Latin rectangles.
[ "1", "-1", "-1", "2", "49", "629", "6961", "38366", "-1899687", "-133065253", "-6482111309", "-281940658286", "-10702380933551", "-247708227641863", "14512103549430397", "3377044611825908414", "433180638973276282801", "47474992085447610990231" ]
[ "sign", "more" ]
32
0
5
null
[ "M2171", "N0867" ]
N. J. A. Sloane
2022-02-01T23:30:46
oeisdata/seq/A001/A001568.seq
b53c9c96e8f1cab42fd338c904bdc214
A001569
Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*(1-exp(x))^(1/2)).
[ "1", "-1", "-1", "2", "37", "329", "1501", "-31354", "-1451967", "-39284461", "-737652869", "560823394", "1103386777549", "82520245792997", "4398448305245905", "168910341581721494", "998428794798272641", "-720450682719825322809", "-105099789680808769094057", "-10594247095804692725600734" ]
[ "sign", "easy" ]
35
0
5
null
[ "M2161", "N0861" ]
N. J. A. Sloane
2021-12-26T21:04:49
oeisdata/seq/A001/A001569.seq
5e8610db6437c001b6d05707712dd0e1
A001570
Numbers k such that k^2 is centered hexagonal.
[ "1", "13", "181", "2521", "35113", "489061", "6811741", "94875313", "1321442641", "18405321661", "256353060613", "3570537526921", "49731172316281", "692665874901013", "9647591076297901", "134373609193269601", "1871582937629476513", "26067787517619401581", "363077442309042145621" ]
[ "nonn", "easy", "nice" ]
148
0
5
[ "A001075", "A001570", "A001921", "A001922", "A003500", "A006051", "A007655", "A028231", "A076139", "A076140", "A077416", "A077417", "A094954", "A102871", "A122571", "A188646", "A238379", "A302329" ]
[ "M4915", "N2108" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001570.seq
0492dd4e6d7fe2dd00308a3369ba40c8
A001571
a(n) = 4*a(n-1) - a(n-2) + 1, with a(0) = 0, a(1) = 2.
[ "0", "2", "9", "35", "132", "494", "1845", "6887", "25704", "95930", "358017", "1336139", "4986540", "18610022", "69453549", "259204175", "967363152", "3610248434", "13473630585", "50284273907", "187663465044", "700369586270", "2613814880037", "9754889933879", "36405744855480", "135868089488042" ]
[ "nonn", "easy" ]
104
0
5
[ "A001353", "A001571", "A001834", "A061278", "A071954", "A082840" ]
[ "M1928", "N0762" ]
N. J. A. Sloane
2023-12-27T11:20:44
oeisdata/seq/A001/A001571.seq
bbf8c396c090f6781762dad16a186a7d
A001572
Related to series-parallel networks.
[ "1", "1", "1", "1", "3", "5", "17", "41", "127", "365", "1119", "3413", "10685", "33561", "106827", "342129", "1104347", "3584649", "11701369", "38374065", "126395259", "417908329", "1386618307", "4615388353", "15407188529", "51569669429", "173033992311", "581905285089", "1961034571967" ]
[ "nonn", "easy" ]
28
0
5
[ "A000084", "A001572", "A144962" ]
[ "M2500", "N0989" ]
N. J. A. Sloane
2021-06-04T22:42:46
oeisdata/seq/A001/A001572.seq
ccea3a7a19eeefdf71491ddd032b7843
A001573
Another approximation to A000084(n).
[ "1", "2", "4", "9", "23", "63", "177", "514", "1527", "4625", "14230", "44357", "139779", "444558", "1425151", "4600339", "14939849", "48778197", "160019885", "527200711" ]
[ "nonn", "more" ]
19
0
5
[ "A000084", "A001573", "A058585" ]
[ "M1190", "N0460" ]
N. J. A. Sloane
2015-06-27T15:07:53
oeisdata/seq/A001/A001573.seq
dcc416e647c4ab9ddf516b871b96ccfe
A001574
Colored series-parallel networks.
[ "0", "2", "12", "60", "292", "1438", "7180", "36566" ]
[ "nonn", "more" ]
20
0
5
null
[ "M2029", "N0801" ]
N. J. A. Sloane
2023-01-14T02:09:09
oeisdata/seq/A001/A001574.seq
33a05e0cc7e208deb8e4c944376988c2
A001575
Colored series-parallel networks.
[ "0", "0", "8", "102", "948", "7900", "62928", "491832" ]
[ "nonn", "more" ]
16
0
5
null
[ "M4567", "N1944" ]
N. J. A. Sloane
2023-01-14T02:09:20
oeisdata/seq/A001/A001575.seq
72fe236d1f3fb076f7ed030c6fe2a175
A001576
a(n) = 1^n + 2^n + 4^n.
[ "3", "7", "21", "73", "273", "1057", "4161", "16513", "65793", "262657", "1049601", "4196353", "16781313", "67117057", "268451841", "1073774593", "4295032833", "17180000257", "68719738881", "274878431233", "1099512676353", "4398048608257", "17592190238721", "70368752566273", "281474993487873", "1125899940397057" ]
[ "nonn", "easy" ]
67
0
5
[ "A001550", "A001576", "A001579", "A002061", "A006095", "A022166", "A034513", "A051154", "A074501", "A074580", "A135576", "A135577" ]
null
N. J. A. Sloane
2023-04-27T22:08:06
oeisdata/seq/A001/A001576.seq
5f509d832d3f53272e0c7fa1afd1c9dc
A001577
An operational recurrence.
[ "1", "1", "2", "6", "60", "2880", "2246400", "135862272000", "10376834265907200000", "77540115374348238323712000000000", "71611262431705169979126571320506685849600000000000000", "799595359352229378487949660335170674324575940302246074414582988800000000000000000000000" ]
[ "nice", "easy", "nonn" ]
20
0
5
null
[ "M1718", "N0681" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001577.seq
c3f9527c43e51dbacd935178de3d3807
A001578
Smallest primitive prime factor of Fibonacci number F(n), or 1 if F(n) has no primitive prime factor.
[ "1", "1", "2", "3", "5", "1", "13", "7", "17", "11", "89", "1", "233", "29", "61", "47", "1597", "19", "37", "41", "421", "199", "28657", "23", "3001", "521", "53", "281", "514229", "31", "557", "2207", "19801", "3571", "141961", "107", "73", "9349", "135721", "2161", "2789", "211", "433494437", "43", "109441", "139", "2971215073", "1103", "97", "101" ]
[ "nonn" ]
68
0
5
[ "A000045", "A000057", "A001578", "A061488", "A086597", "A106535", "A262341" ]
[ "M0603", "N0217" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001578.seq
4c726d6f7916e5d47c9119cdbb4c600c
A001579
a(n) = 3^n + 5^n + 6^n.
[ "3", "14", "70", "368", "2002", "11144", "63010", "360248", "2076802", "12050504", "70290850", "411802328", "2421454402", "14282991464", "84472462690", "500716911608", "2973740844802", "17689728038024", "105375041354530", "628434388600088" ]
[ "easy", "nonn" ]
36
0
5
[ "A001550", "A001576", "A001579", "A034513", "A074501", "A074580" ]
null
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001579.seq
31575bc53f6a45cfffa36741a4b980f2
A001580
a(n) = 2^n + n^2.
[ "1", "3", "8", "17", "32", "57", "100", "177", "320", "593", "1124", "2169", "4240", "8361", "16580", "32993", "65792", "131361", "262468", "524649", "1048976", "2097593", "4194788", "8389137", "16777792", "33555057", "67109540", "134218457", "268436240" ]
[ "nonn", "easy" ]
32
0
5
null
null
N. J. A. Sloane
2023-04-23T12:23:28
oeisdata/seq/A001/A001580.seq
5b926512824cc0a2da766568619057b2
A001581
Winning moves in Fibonacci nim.
[ "4", "10", "14", "20", "24", "30", "36", "40", "46", "50", "56", "60", "66", "72", "76", "82", "86", "92", "96", "102", "108", "112", "118", "122", "128", "132", "138", "150", "160", "169", "176", "186", "192", "196", "202", "206", "212", "218", "222", "228", "232", "238", "242", "248", "254", "260", "264", "270", "274", "280", "284", "290", "296", "300", "306", "310" ]
[ "nonn", "nice" ]
57
0
5
[ "A001581", "A030193" ]
[ "M3374", "N1359" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001581.seq
f752dde152b78945fe5da8d066cce7b5
A001582
Product of Fibonacci and Pell numbers.
[ "1", "2", "10", "36", "145", "560", "2197", "8568", "33490", "130790", "510949", "1995840", "7796413", "30454814", "118965250", "464711184", "1815292333", "7091038640", "27699580729", "108202305420", "422668460890", "1651061182538", "6449506621417", "25193576136960" ]
[ "nonn", "easy", "nice" ]
95
0
5
[ "A000045", "A000129", "A001582" ]
[ "M1966", "N0779" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001582.seq
807c2a107080933013aced1279308005
A001583
Artiads: the primes p == 1 (mod 5) for which Fibonacci((p-1)/5) is divisible by p.
[ "211", "281", "421", "461", "521", "691", "881", "991", "1031", "1151", "1511", "1601", "1871", "1951", "2221", "2591", "3001", "3251", "3571", "3851", "4021", "4391", "4441", "4481", "4621", "4651", "4691", "4751", "4871", "5081", "5281", "5381", "5531", "5591", "5641", "5801", "5881", "6011", "6101", "6211", "6271", "6491", "6841" ]
[ "nonn", "nice" ]
111
0
5
[ "A000045", "A001583", "A024894", "A030430", "A047650", "A270798", "A270800" ]
[ "M5413", "N2351" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001583.seq
202e1df01f619b1f38f4c5a50f3e967d
A001584
A generalized Fibonacci sequence.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "4", "4", "4", "7", "7", "8", "12", "12", "16", "21", "21", "31", "37", "38", "58", "65", "71", "106", "114", "135", "191", "201", "257", "341", "359", "485", "605", "652", "904", "1070", "1202", "1664", "1894", "2237", "3029", "3370", "4176", "5464", "6048", "7779", "9793", "10963", "14411", "17492", "20054", "26507", "31239", "36924", "48396" ]
[ "nonn", "easy" ]
47
0
5
[ "A001584", "A017817" ]
[ "M0235", "N0080" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001584.seq
7d20ca9235092558e5a39ab911b71bcb
A001585
a(n) = 3^n + n^3.
[ "1", "4", "17", "54", "145", "368", "945", "2530", "7073", "20412", "60049", "178478", "533169", "1596520", "4785713", "14352282", "43050817", "129145076", "387426321", "1162268326", "3486792401", "10460362464", "31381070257", "94143190994", "282429550305", "847288625068" ]
[ "nonn", "easy" ]
23
0
5
[ "A001580", "A001585" ]
null
N. J. A. Sloane
2023-06-09T07:49:01
oeisdata/seq/A001/A001585.seq
8b1cf00d2cf8fdb3d8868050c019ed8c
A001586
Generalized Euler numbers, or Springer numbers.
[ "1", "1", "3", "11", "57", "361", "2763", "24611", "250737", "2873041", "36581523", "512343611", "7828053417", "129570724921", "2309644635483", "44110959165011", "898621108880097", "19450718635716001", "445777636063460643", "10784052561125704811", "274613643571568682777", "7342627959965776406281" ]
[ "nonn", "easy", "nice" ]
247
0
5
[ "A000281", "A000464", "A001586", "A007836", "A046802", "A079858", "A081658", "A098432", "A153641", "A185417", "A185418", "A212435", "A349264", "A349271" ]
[ "M2908", "N1169" ]
N. J. A. Sloane
2025-01-19T14:28:04
oeisdata/seq/A001/A001586.seq
d4618db5f21d1cb9ad8e6ef1e10be7c2
A001587
Generalized Euler numbers.
[ "2", "6", "46", "522", "7970", "152166", "3487246", "93241002", "2849229890", "97949265606", "3741386059246", "157201459863882", "7205584123783010", "357802951084619046", "19133892392367261646", "1096291279711115037162", "67000387673723462963330", "4350684698032741048452486", "299131045427247559446422446" ]
[ "nonn" ]
60
0
5
[ "A000111", "A000192", "A000411", "A001587", "A225147", "A349264" ]
[ "M1715", "N0679" ]
N. J. A. Sloane
2021-11-22T04:03:38
oeisdata/seq/A001/A001587.seq
09eefb178693406fd1cfed1ee51abfb8
A001588
a(n) = a(n-1) + a(n-2) - 1.
[ "1", "3", "3", "5", "7", "11", "17", "27", "43", "69", "111", "179", "289", "467", "755", "1221", "1975", "3195", "5169", "8363", "13531", "21893", "35423", "57315", "92737", "150051", "242787", "392837", "635623", "1028459", "1664081", "2692539", "4356619", "7049157", "11405775", "18454931", "29860705", "48315635" ]
[ "nonn", "easy" ]
90
0
5
[ "A000045", "A001588", "A001611", "A001906" ]
[ "M2279", "N0901" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001588.seq
88276ed424b05213830e0b131850c838
A001589
a(n) = 4^n + n^4.
[ "1", "5", "32", "145", "512", "1649", "5392", "18785", "69632", "268705", "1058576", "4208945", "16797952", "67137425", "268473872", "1073792449", "4295032832", "17179952705", "68719581712", "274878037265", "1099511787776", "4398046705585", "17592186278672" ]
[ "nonn", "easy" ]
54
0
5
[ "A001580", "A001585", "A001589" ]
null
N. J. A. Sloane
2023-03-06T10:06:03
oeisdata/seq/A001/A001589.seq
0dafb1d78fb2b8676655bbda5e7fb033
A001590
Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=0, a(1)=1, a(2)=0.
[ "0", "1", "0", "1", "2", "3", "6", "11", "20", "37", "68", "125", "230", "423", "778", "1431", "2632", "4841", "8904", "16377", "30122", "55403", "101902", "187427", "344732", "634061", "1166220", "2145013", "3945294", "7256527", "13346834", "24548655", "45152016", "83047505", "152748176", "280947697", "516743378", "950439251" ]
[ "nonn", "easy" ]
206
0
5
[ "A000045", "A000073", "A001590", "A027053", "A027907", "A078042", "A145579", "A278038" ]
[ "M0784", "N0296" ]
N. J. A. Sloane
2025-03-28T06:50:10
oeisdata/seq/A001/A001590.seq
2a2b03ec0b432c532866c163ec375027
A001591
Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), a(0)=a(1)=a(2)=a(3)=0, a(4)=1.
[ "0", "0", "0", "0", "1", "1", "2", "4", "8", "16", "31", "61", "120", "236", "464", "912", "1793", "3525", "6930", "13624", "26784", "52656", "103519", "203513", "400096", "786568", "1546352", "3040048", "5976577", "11749641", "23099186", "45411804", "89277256", "175514464", "345052351", "678355061", "1333610936", "2621810068" ]
[ "nonn", "easy" ]
243
0
5
[ "A001591", "A035343", "A048887", "A074048", "A074062", "A092921", "A106303", "A123126", "A123127" ]
[ "M1122", "N0429" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001591.seq
6b47ff5d253ccab38d0b6a2696fce256
A001592
Hexanacci numbers: a(n+1) = a(n)+...+a(n-5) with a(0)=...=a(4)=0, a(5)=1.
[ "0", "0", "0", "0", "0", "1", "1", "2", "4", "8", "16", "32", "63", "125", "248", "492", "976", "1936", "3840", "7617", "15109", "29970", "59448", "117920", "233904", "463968", "920319", "1825529", "3621088", "7182728", "14247536", "28261168", "56058368", "111196417", "220567305", "437513522", "867844316", "1721441096", "3414621024" ]
[ "nonn", "easy" ]
152
0
5
[ "A001592", "A048887", "A092921" ]
[ "M1128", "N0431" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001592.seq
ba30738da6e23bb6c4f06f917b77e426
A001593
a(n) = 5^n + n^5.
[ "1", "6", "57", "368", "1649", "6250", "23401", "94932", "423393", "2012174", "9865625", "48989176", "244389457", "1221074418", "6104053449", "30518337500", "152588939201", "762940872982", "3814699155193", "19073488804224", "95367434840625", "476837162287226", "2384185796169257", "11920928961514468" ]
[ "nonn", "easy" ]
33
0
5
[ "A001580", "A001585", "A001589", "A001593" ]
null
N. J. A. Sloane
2022-09-08T08:44:29
oeisdata/seq/A001/A001593.seq
4d62a66837f17d0666c8373b9318d559
A001594
a(n) = 6^n + n^6.
[ "1", "7", "100", "945", "5392", "23401", "93312", "397585", "1941760", "10609137", "61466176", "364568617", "2179768320", "13065520825", "78371693632", "470196375201", "2821126684672", "16926683582305", "101559990680640", "609359787056377" ]
[ "nonn", "easy" ]
31
0
5
[ "A001580", "A001585", "A001589", "A001593", "A001594", "A001596", "A177068", "A177069", "A185277", "A198401" ]
null
N. J. A. Sloane
2023-01-07T13:17:52
oeisdata/seq/A001/A001594.seq
02976e9c5960bcc8dae2210e311f6ddd
A001595
a(n) = a(n-1) + a(n-2) + 1, with a(0) = a(1) = 1.
[ "1", "1", "3", "5", "9", "15", "25", "41", "67", "109", "177", "287", "465", "753", "1219", "1973", "3193", "5167", "8361", "13529", "21891", "35421", "57313", "92735", "150049", "242785", "392835", "635621", "1028457", "1664079", "2692537", "4356617", "7049155", "11405773", "18454929", "29860703", "48315633", "78176337" ]
[ "nonn", "easy", "nice" ]
165
0
5
[ "A000045", "A000071", "A001595", "A006355", "A033538", "A049112", "A049114", "A101220", "A109754", "A128587" ]
[ "M2453", "N0974" ]
N. J. A. Sloane
2025-03-03T12:43:33
oeisdata/seq/A001/A001595.seq
bffb8c5e7c62e37013d29920d65ba012
A001596
a(n) = 7^n + n^7.
[ "1", "8", "177", "2530", "18785", "94932", "397585", "1647086", "7861953", "45136576", "292475249", "1996813914", "13877119009", "96951758924", "678328486353", "4747732369318", "33233199005057", "232630924325880", "1628414210130481" ]
[ "nonn", "easy" ]
27
0
5
[ "A001580", "A001585", "A001589", "A001593", "A001594", "A001596" ]
null
N. J. A. Sloane
2022-09-08T08:44:29
oeisdata/seq/A001/A001596.seq
58e75dd8ec3d1fa27d3ff7c8eaea479f
A001597
Perfect powers: m^k where m > 0 and k >= 2.
[ "1", "4", "8", "9", "16", "25", "27", "32", "36", "49", "64", "81", "100", "121", "125", "128", "144", "169", "196", "216", "225", "243", "256", "289", "324", "343", "361", "400", "441", "484", "512", "529", "576", "625", "676", "729", "784", "841", "900", "961", "1000", "1024", "1089", "1156", "1225", "1296", "1331", "1369", "1444", "1521", "1600", "1681", "1728", "1764" ]
[ "nonn", "easy", "nice", "changed" ]
244
0
5
[ "A000961", "A001597", "A007916", "A023055", "A023057", "A025475", "A025478", "A053289", "A070428", "A072102", "A072103", "A072777", "A074981", "A075090", "A075109", "A076404", "A089579", "A089580", "A097054", "A239728", "A239870", "A246547", "A246655" ]
[ "M3326", "N1336" ]
N. J. A. Sloane
2025-04-19T19:36:53
oeisdata/seq/A001/A001597.seq
7e034992c89e72182c3a7061ca068a44
A001598
Number of terms in {b(1)..b(n)} relatively prime to b(n), where b(n) = A001597(n).
[ "1", "1", "1", "3", "2", "5", "5", "4", "2", "9", "5", "8", "5", "13", "12", "8", "5", "17", "8", "6", "11", "14", "11", "23", "7", "23", "26", "11", "16", "14", "15", "31", "10", "28", "16", "24", "15", "37", "9", "39", "16", "20", "27", "20", "31", "14", "43", "47", "23", "32", "20", "51", "17", "14", "54", "24", "30", "28", "27", "40", "57", "61", "20", "56", "26", "42", "30", "28", "68", "22" ]
[ "nonn", "easy" ]
20
0
5
null
[ "M2244", "N0891" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A001/A001598.seq
d34795a823d0fd65d32525d00627550a
A001599
Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.
[ "1", "6", "28", "140", "270", "496", "672", "1638", "2970", "6200", "8128", "8190", "18600", "18620", "27846", "30240", "32760", "55860", "105664", "117800", "167400", "173600", "237510", "242060", "332640", "360360", "539400", "695520", "726180", "753480", "950976", "1089270", "1421280", "1539720" ]
[ "nonn", "nice" ]
173
0
5
[ "A000005", "A000203", "A000290", "A001599", "A001600", "A003601", "A007340", "A007691", "A027750", "A035527", "A053783", "A074247", "A090240", "A090945" ]
[ "M4185", "N1743" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001599.seq
fea7a055dcca5782617cca3e5a5babed
A001600
Harmonic means of divisors of harmonic numbers.
[ "1", "2", "3", "5", "6", "5", "8", "9", "11", "10", "7", "15", "15", "14", "17", "24", "24", "21", "13", "19", "27", "25", "29", "26", "44", "44", "29", "46", "39", "46", "27", "42", "47", "47", "54", "35", "41", "60", "51", "37", "48", "45", "49", "50", "49", "53", "77", "86", "86", "51", "96", "75", "70", "80", "99", "110", "81", "84", "13", "102", "82", "96", "114", "53", "108", "115", "105", "116", "91", "85", "105" ]
[ "nonn", "nice", "easy" ]
47
0
5
[ "A001599", "A001600", "A090240" ]
[ "M0609", "N0220" ]
N. J. A. Sloane
2021-12-19T10:02:25
oeisdata/seq/A001/A001600.seq
c4c01374ef681d8bb2ff5db1ea5d74f4