Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
sequencelengths
1
348
keywords
sequencelengths
1
8
score
int64
1
2.31k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
sequencelengths
1
128
⌀
former_ids
sequencelengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-28 00:58:08
filename
stringlengths
29
29
hash
stringlengths
32
32
A007001
Trajectory of 1 under the morphism 1 -> 12, 2 -> 123, 3 -> 1234, etc.
[ "1", "2", "1", "2", "3", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "1", "2", "3", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "3", "4", "5", "1", "2", "1", "2", "3", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "1", "2", "3", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "3", "4", "5", "1", "2", "1", "2", "3", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "1", "2", "3", "1", "2" ]
[ "easy", "nonn", "nice" ]
56
1
2
[ "A000108", "A000245", "A007001", "A076050", "A080336", "A085180", "A085182", "A085197" ]
[ "M0108" ]
N. J. A. Sloane, Mira Bernstein, James Propp
2021-02-21T14:13:10
oeisdata/seq/A007/A007001.seq
e17e25693dcc6cb9f72b7322c4c421ae
A007002
Sum of degrees of irreducible representations of alternating group A_n.
[ "1", "1", "3", "6", "16", "46", "126", "448", "1366", "5356", "18568", "76296", "297012", "1264264", "5412928", "23928024", "110468806", "509578384", "2495966844", "12051904744", "61878848596", "312943394336", "1670571625528", "8836179426416", "48794206157176", "269194017597376", "1533137311902576" ]
[ "nonn" ]
15
1
3
null
[ "M2592" ]
N. J. A. Sloane.
2024-06-14T22:31:09
oeisdata/seq/A007/A007002.seq
3f983f0bb4ec830d854dfacc3d493a5a
A007003
Euler transform of numbers of preferential arrangements.
[ "1", "2", "5", "19", "97", "658", "5458", "53628", "606871", "7766312", "110811174", "1743359979", "29972475254", "558940415943", "11235765584497", "242168565186139", "5570683131749362", "136215122718876230", "3527978807819506487", "96480528944412962039", "2778048842021042988465" ]
[ "nonn" ]
22
0
2
[ "A000670", "A007003", "A290352" ]
null
N. J. A. Sloane.
2017-09-14T16:33:48
oeisdata/seq/A007/A007003.seq
86a8f23b918baa3589bdfd68d7d14b9d
A007004
a(n) = (3*n)! / ((n+1)*(n!)^3).
[ "1", "3", "30", "420", "6930", "126126", "2450448", "49884120", "1051723530", "22787343150", "504636071940", "11377249621920", "260363981732400", "6034149862347600", "141371511060715200", "3343436236585914480", "79726203788589122490", "1914992149823954412750", "46295775130831740013500" ]
[ "nonn", "changed" ]
75
0
2
[ "A000108", "A007004", "A060693", "A215561" ]
[ "M3125" ]
N. J. A. Sloane, James Propp
2025-04-19T03:25:25
oeisdata/seq/A007/A007004.seq
10c14948963a7338f8afe73ddfa67048
A007005
Number of characters in the French spelling of n, including spaces and hyphens.
[ "4", "2", "4", "5", "6", "4", "3", "4", "4", "4", "3", "4", "5", "6", "8", "6", "5", "8", "8", "8", "5", "11", "10", "11", "12", "10", "9", "10", "10", "10", "6", "12", "11", "12", "13", "11", "10", "11", "11", "11", "8", "14", "13", "14", "15", "13", "12", "13", "13", "13", "9", "15", "14", "15", "16", "14", "13", "14", "14", "14", "8", "14", "13", "14", "15", "13", "12", "13", "13", "13", "12", "16", "14", "15", "17", "15", "14" ]
[ "nonn", "word", "easy", "nice" ]
50
0
1
[ "A005589", "A007005", "A007208", "A052360", "A167507" ]
[ "M0942" ]
Simon Plouffe
2024-07-10T20:06:21
oeisdata/seq/A007/A007005.seq
d6864f5f78a15973626354168aad9085
A007006
Number of edges in graph of maximal intersecting families of sets.
[ "0", "1", "3", "16", "185", "10886", "10552451" ]
[ "nonn", "more" ]
21
1
3
null
[ "M3031" ]
Daniel E. Loeb
2023-09-17T12:29:28
oeisdata/seq/A007/A007006.seq
c3b2be39d0812a3a0d47e7aec376beb8
A007007
Valence of graph of maximal intersecting families of sets.
[ "0", "1", "3", "4", "10", "15", "35", "56", "126", "210", "462", "792", "1716", "3003", "6435", "11440", "24310", "43758", "92378", "167960", "352716", "646646", "1352078", "2496144", "5200300", "9657700", "20058300", "37442160", "77558760", "145422675", "300540195", "565722720", "1166803110", "2203961430" ]
[ "nonn", "nice" ]
25
1
3
[ "A001206", "A007006", "A007007", "A007008" ]
[ "M2361" ]
Daniel E. Loeb
2017-09-19T10:17:38
oeisdata/seq/A007/A007007.seq
dc8f21933b866992d3e9abe155419ebf
A007008
Chvatal conjecture for radius of graph of maximal intersecting sets.
[ "0", "1", "1", "3", "5", "11", "22", "47", "93", "193", "386", "793", "1586", "3238", "6476", "13167", "26333", "53381", "106762", "215955", "431910", "872218", "1744436", "3518265", "7036530", "14177066", "28354132", "57079714", "114159428", "229656076", "459312152", "923471727", "1846943453", "3711565741", "7423131482" ]
[ "nonn" ]
38
1
4
[ "A000346", "A001206", "A007007", "A007008" ]
[ "M2484" ]
Daniel E. Loeb
2023-09-17T12:29:44
oeisdata/seq/A007/A007008.seq
018ae33ab273f2a1588568d89668e1bf
A007009
Number of 3-voter voting schemes with n linearly ranked choices.
[ "1", "4", "12", "27", "54", "96", "160", "250", "375", "540", "756", "1029", "1372", "1792", "2304", "2916", "3645", "4500", "5500", "6655", "7986", "9504", "11232", "13182", "15379", "17836", "20580", "23625", "27000", "30720", "34816", "39304", "44217", "49572", "55404", "61731", "68590", "76000", "84000", "92610", "101871", "111804" ]
[ "nonn", "easy" ]
57
1
2
[ "A007009", "A034828" ]
[ "M3435" ]
Daniel E. Loeb
2023-04-14T15:55:07
oeisdata/seq/A007/A007009.seq
816e26ce985bbdc210221f05e7d3bc58
A007010
Number of 4-voter voting schemes with n linearly ranked choices.
[ "1", "12", "81", "372", "1332", "3984", "10420", "24540", "53145", "107436", "205065", "372792", "649936", "1092672", "1779408", "2817288", "4350105", "6567660", "9716905", "14114892", "20163924", "28368912", "39357396", "53902212", "72947329", "97636812", "129347505", "169725360", "220726080", "284659968", "364241728" ]
[ "nonn", "easy" ]
22
1
2
null
[ "M4851" ]
Daniel E. Loeb
2023-02-12T16:16:00
oeisdata/seq/A007/A007010.seq
ecd019032225d60a313e2516eb0921bb
A007011
a(n) = smallest pseudoprime to base 2 with n prime factors.
[ "341", "561", "11305", "825265", "45593065", "370851481", "38504389105", "7550611589521", "277960972890601", "32918038719446881", "1730865304568301265", "606395069520916762801", "59989606772480422038001", "6149883077429715389052001", "540513705778955131306570201", "35237869211718889547310642241" ]
[ "nonn", "nice" ]
31
2
1
[ "A007011", "A007535" ]
[ "M5444" ]
Richard Pinch
2023-03-05T01:28:35
oeisdata/seq/A007/A007011.seq
2c6923a81bdfd233a0b660f6465e2a61
A007012
a(n) is number of k for which C(n,k) is not divisible by n.
[ "1", "0", "2", "2", "3", "2", "5", "2", "5", "4", "5", "2", "8", "2", "9", "8", "9", "2", "9", "2", "11", "8", "9", "2", "15", "6", "9", "10", "15", "2", "20", "2", "17", "8", "5", "10", "15", "2", "9", "10", "19", "2", "23", "2", "19", "20", "17", "2", "29", "8", "17", "20", "19", "2", "29", "10", "24", "8", "17", "2", "35", "2", "33", "18", "33", "16", "19", "2", "11", "20", "27", "2", "33", "2", "9", "30", "19", "16", "41", "2", "31", "28", "9", "2", "32", "16" ]
[ "nonn" ]
24
0
3
[ "A007012", "A020475", "A053200" ]
[ "M0248" ]
N. J. A. Sloane
2022-11-18T23:36:50
oeisdata/seq/A007/A007012.seq
3a5071366f64253b9451946b6c9a6722
A007013
Catalan-Mersenne numbers: a(0) = 2; for n >= 0, a(n+1) = 2^a(n) - 1.
[ "2", "3", "7", "127", "170141183460469231731687303715884105727" ]
[ "nonn" ]
134
0
1
[ "A000668", "A001567", "A006050", "A007013", "A014221", "A180094" ]
[ "M0866" ]
N. J. A. Sloane, Nik Lygeros (webmaster(AT)lygeros.org)
2025-02-16T08:32:31
oeisdata/seq/A007/A007013.seq
a74e065ccbf6d7a5c5d8bb473b9b90eb
A007014
Largest prime <= Product prime(k).
[ "2", "5", "29", "199", "2309", "30029", "510481", "9699667", "223092827", "6469693189", "200560490057", "7420738134751", "304250263527209", "13082761331669941", "614889782588491343", "32589158477190044657", "1922760350154212638963", "117288381359406970983181", "7858321551080267055878989" ]
[ "nonn" ]
30
1
1
[ "A000849", "A002110", "A007014", "A038710", "A057705", "A151799" ]
[ "M1546" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2023-07-18T06:51:29
oeisdata/seq/A007/A007014.seq
44ebb80b2faac224cf69a540de66662d
A007015
a(n) = smallest k such that phi(n+k) = phi(k).
[ "1", "4", "3", "8", "5", "24", "5", "13", "9", "20", "7", "48", "13", "16", "13", "26", "17", "52", "19", "37", "21", "44", "13", "96", "25", "34", "27", "32", "13", "124", "17", "52", "33", "41", "19", "104", "35", "52", "37", "65", "25", "123", "17", "73", "39", "92", "41", "183", "35", "76", "39", "68", "53", "156", "35", "64", "57", "116", "41", "248", "61", "73", "61", "104", "65", "144", "67", "82" ]
[ "nonn", "nice" ]
51
1
2
[ "A000010", "A007015" ]
[ "M3212" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2021-12-22T00:04:26
oeisdata/seq/A007/A007015.seq
5087f3c23e24b1612ee86fba89fbc1cf
A007016
Number of permutations of length n with 1 fixed and 1 reflected point.
[ "0", "1", "0", "0", "8", "20", "96", "656", "5568", "48912", "494080", "5383552", "65097600", "840566080", "11833898496", "176621049600", "2838024476672", "48060623405312", "868000333234176", "16441638519762944", "329723762151352320", "6907027877807330304" ]
[ "nonn", "easy" ]
50
0
5
[ "A003471", "A007016", "A064280" ]
[ "M4491" ]
N. J. A. Sloane
2025-02-27T04:43:04
oeisdata/seq/A007/A007016.seq
b9dd73a359cc2f679fe6b18913ed306c
A007017
Number of motifs in triangular window of side n.
[ "1", "3", "12", "65", "480", "4851", "67256", "1281258", "33576120", "1211321683", "60197760876", "4122762095127", "389255776509600", "50680509287223315", "9101288287232978112", "2254758094831392182844" ]
[ "nonn" ]
16
0
2
null
[ "M2935" ]
G. Rauzy
2017-11-07T18:18:17
oeisdata/seq/A007/A007017.seq
f750378622624b2467e35942a89e71f1
A007018
a(n) = a(n-1)^2 + a(n-1), a(0)=1.
[ "1", "2", "6", "42", "1806", "3263442", "10650056950806", "113423713055421844361000442", "12864938683278671740537145998360961546653259485195806" ]
[ "nonn", "nice", "easy" ]
229
0
2
[ "A000058", "A003687", "A004168", "A007018", "A011782", "A077125", "A100016", "A117805", "A118227", "A122888", "A371321" ]
[ "M1713" ]
N. J. A. Sloane
2025-03-01T03:19:02
oeisdata/seq/A007/A007018.seq
f08c9736a66cef273355f872dcbafa48
A007019
a(n) = (2n+1)! / 2^n.
[ "1", "3", "30", "630", "22680", "1247400", "97297200", "10216206000", "1389404016000", "237588086736000", "49893498214560000", "12623055048283680000", "3786916514485104000000", "1329207696584271504000000", "539658324813214230624000000", "250941121038144617240160000000", "132496911908140357902804480000000" ]
[ "nonn", "easy" ]
101
0
2
[ "A002067", "A007019", "A007680" ]
[ "M3126" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007019.seq
68525409c427e406a2471d1d6e1bf624
A007020
Maximal planar degree sequences with n nodes.
[ "1", "1", "1", "2", "5", "13", "33", "85", "199", "445", "947", "1909", "3713", "7006", "12765", "22764", "39540" ]
[ "nonn", "more" ]
17
3
4
[ "A000109", "A007020" ]
[ "M1437" ]
N. J. A. Sloane
2017-09-17T16:30:44
oeisdata/seq/A007/A007020.seq
3aba0329f2a1044114ce051ea62926ac
A007021
Number of 4-connected simplicial polyhedra with n nodes.
[ "1", "1", "1", "1", "1", "2", "4", "10", "25", "87", "313", "1357", "6244", "30926", "158428", "836749", "4504607", "24649284", "136610879", "765598927", "4332047595", "24724362117", "142205424580", "823687567019", "4801749063379" ]
[ "nonn", "more" ]
45
3
6
[ "A000109", "A007021", "A007027", "A111358" ]
[ "M1214" ]
N. J. A. Sloane
2024-11-12T09:02:07
oeisdata/seq/A007/A007021.seq
7c533894f9372266d9b9a59e42a67c0c
A007022
Number of 4-regular polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "1", "0", "1", "1", "3", "3", "11", "18", "58", "139", "451", "1326", "4461", "14554", "49957", "171159", "598102", "2098675", "7437910", "26490072", "94944685", "341867921", "1236864842", "4493270976", "16387852863", "59985464681", "220320405895", "811796327750", "3000183106119" ]
[ "nonn" ]
73
1
10
[ "A000944", "A007022", "A072552", "A078666", "A078672", "A111361", "A113204", "A292515" ]
[ "M2290" ]
N. J. A. Sloane, Apr 28 1994
2024-05-14T02:23:44
oeisdata/seq/A007/A007022.seq
1ce862884291c09a988b9c86740e526a
A007023
Number of 4-connected 4-regular polyhedra with n nodes.
[ "1", "0", "1", "0", "3", "1", "8", "7", "37", "55", "220", "499", "1862", "5174", "18258", "57107", "198474" ]
[ "nonn", "more" ]
16
6
5
[ "A007022", "A007023", "A007027" ]
[ "M2230" ]
N. J. A. Sloane
2019-10-11T08:51:37
oeisdata/seq/A007/A007023.seq
68e23d9caeaeb3b8509ad492d21abec8
A007024
Number of polyhedral graphs with n faces and minimal degree 4.
[ "0", "0", "0", "0", "1", "0", "2", "2", "9", "17", "77", "261", "1265", "5852", "29916", "153507", "810351" ]
[ "nonn" ]
12
4
7
null
[ "M0382" ]
N. J. A. Sloane.
2017-09-18T21:02:05
oeisdata/seq/A007/A007024.seq
65c7e2e8cdd81051a78c0a4779dd5536
A007025
Number of polyhedral graphs with n nodes and minimal degree 4.
[ "0", "0", "1", "1", "4", "14", "67", "428", "3515", "31763", "307543", "3064701", "31199068", "322264655", "3369911732", "35611596455", "379881408164", "4086847012014", "44308209298480" ]
[ "nonn", "more", "hard" ]
30
4
5
null
[ "M3487" ]
N. J. A. Sloane
2021-12-26T21:38:09
oeisdata/seq/A007/A007025.seq
f1ef29c0b4081ca66be4ff58916c0937
A007026
Number of 4-connected polyhedral graphs with n faces.
[ "1", "0", "0", "0", "1", "0", "2", "1", "8", "11", "56", "160", "777", "3259", "16065", "77871" ]
[ "nonn" ]
14
4
7
null
[ "M0182" ]
N. J. A. Sloane.
2017-09-20T03:56:15
oeisdata/seq/A007/A007026.seq
fa65a82eef04c2ecc24b5c38fcd091e3
A007027
Number of 4-connected polyhedral graphs with n nodes.
[ "1", "0", "1", "1", "4", "10", "53", "292", "2224", "18493", "167504", "1571020", "15151289", "148864939", "1485904672", "15028654628", "153781899708", "1589921572902", "16591187039082" ]
[ "nonn", "hard" ]
15
4
5
null
[ "M3402" ]
N. J. A. Sloane
2024-02-27T21:03:51
oeisdata/seq/A007/A007027.seq
fd07042fba28bf190803499a6265d820
A007028
Number of bipartite polyhedral graphs with n nodes.
[ "1", "0", "1", "1", "5", "5", "21", "40", "176", "500", "2053", "7532", "31206", "124552", "521332", "2167599", "9183879", "38965327", "166956753", "718004565", "3107450143", "13502835176", "58956369552", "258398671525" ]
[ "nonn" ]
22
8
5
null
[ "M3743" ]
N. J. A. Sloane.
2024-05-27T22:40:43
oeisdata/seq/A007/A007028.seq
1ba2ec9fb3ea5a99d3e923cbac31aee9
A007029
Number of bipartite polyhedral graphs with n faces.
[ "1", "0", "2", "3", "10", "27", "126", "593", "3411", "20369", "129403" ]
[ "nonn" ]
11
6
3
null
[ "M0905" ]
N. J. A. Sloane.
2017-09-20T19:21:27
oeisdata/seq/A007/A007029.seq
bdad499b85ceec38149c3aea6a2d7830
A007030
Non-Hamiltonian simplicial polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "2", "30", "239", "2369", "22039", "205663", "1879665", "16999932", "152227187", "1353996482" ]
[ "nonn", "hard", "more" ]
36
1
12
[ "A000109", "A007030", "A115340" ]
[ "M2152" ]
N. J. A. Sloane.
2025-02-16T08:32:31
oeisdata/seq/A007/A007030.seq
526bc000a20fdd8596dd211a0a552f94
A007031
Non-Hamiltonian 1-tough simplicial polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "6", "72", "847", "9801" ]
[ "nonn", "hard", "more" ]
16
1
14
[ "A007030", "A007031" ]
[ "M4278" ]
N. J. A. Sloane.
2021-08-07T17:21:42
oeisdata/seq/A007/A007031.seq
13c632b8f96c1d4f449f52bc6682695e
A007032
Number of non-Hamiltonian polyhedra with n faces.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "8", "135", "2557" ]
[ "nonn" ]
8
1
10
null
[ "M4574" ]
N. J. A. Sloane.
2025-02-16T08:32:31
oeisdata/seq/A007/A007032.seq
6f1c0eb48d56afcb2486ee0a98362784
A007033
Non-Hamiltonian polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "74", "1600", "43984", "1032208", "22960220" ]
[ "nonn", "hard" ]
17
1
11
null
[ "M5351" ]
N. J. A. Sloane.
2025-02-16T08:32:31
oeisdata/seq/A007/A007033.seq
1a0bc1fdcb8695481311b24927b9a7a7
A007034
Noncircumscribable simplicial polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "1", "2", "8", "35", "168", "999", "6340", "43133", "305271", "2231377" ]
[ "nonn" ]
7
1
8
null
[ "M1854" ]
N. J. A. Sloane.
2012-03-30T16:45:06
oeisdata/seq/A007/A007034.seq
85423d9b24ec8f8e67dabc5af927858b
A007035
Number of non-1-Hamiltonian simplicial polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "0", "1", "1", "10", "53", "383", "2809", "21884", "172214", "1374908" ]
[ "nonn", "more" ]
12
1
10
null
[ "M4711" ]
N. J. A. Sloane.
2017-09-27T09:28:06
oeisdata/seq/A007/A007035.seq
233a10fd1912181a3febe640b92db5c2
A007036
Number of 1-supertough but non-1-Hamiltonian simplicial polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "5", "40", "343", "2979", "25950", "224773" ]
[ "nonn", "hard" ]
10
1
11
null
[ "M3990" ]
N. J. A. Sloane.
2017-09-27T16:09:33
oeisdata/seq/A007/A007036.seq
f3f2eba1923fdd3d56eed8b71027e72f
A007037
Noninscribable simplicial polyhedra with n nodes.
[ "0", "0", "0", "0", "0", "0", "0", "1", "1", "9", "48", "343", "2466", "18905" ]
[ "nonn" ]
6
1
10
null
[ "M4629" ]
N. J. A. Sloane.
2012-03-30T16:45:06
oeisdata/seq/A007/A007037.seq
d84146889b32a4156bb1fae1bb1f9337
A007038
Theta series of 20-dimensional lattice R_20 with det 1024 and minimal norm 4.
[ "1", "0", "3960", "168960", "2094840", "16625664", "80652000", "343664640", "1073639160", "3299450880", "8000389584", "20081064960", "41278084320", "90307768320", "165298921920", "327406565376", "549720551160", "1009911767040", "1587054299160", "2748047385600", "4095742639824", "6764533923840" ]
[ "nonn" ]
29
0
3
[ "A007038", "A034599" ]
null
N. J. A. Sloane
2023-05-13T06:21:40
oeisdata/seq/A007/A007038.seq
bdf64415d517a02c74003aecf83e5db6
A007039
Number of cyclic binary n-bit strings with no alternating substring of length > 2.
[ "2", "2", "2", "6", "12", "20", "30", "46", "74", "122", "200", "324", "522", "842", "1362", "2206", "3572", "5780", "9350", "15126", "24474", "39602", "64080", "103684", "167762", "271442", "439202", "710646", "1149852", "1860500", "3010350", "4870846", "7881194", "12752042", "20633240", "33385284", "54018522", "87403802", "141422322" ]
[ "nonn", "easy", "eigen" ]
61
1
1
[ "A000032", "A007039", "A007040", "A057079", "A111734" ]
[ "M0241" ]
N. J. A. Sloane
2025-03-09T12:25:30
oeisdata/seq/A007/A007039.seq
25db6faa97381de4c72e61311ec21e7e
A007040
Number of (marked) cyclic n-bit binary strings containing no runs of length > 2.
[ "2", "2", "6", "6", "10", "20", "28", "46", "78", "122", "198", "324", "520", "842", "1366", "2206", "3570", "5780", "9348", "15126", "24478", "39602", "64078", "103684", "167760", "271442", "439206", "710646", "1149850", "1860500", "3010348", "4870846", "7881198", "12752042", "20633238", "33385284", "54018520" ]
[ "nonn", "nice", "easy" ]
142
1
1
[ "A000032", "A007039", "A007040", "A316660" ]
[ "M0354" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007040.seq
31999dd454c87f16a500259a1185ed6e
A007041
State assignments for n-state machine.
[ "2", "12", "12", "1120", "3360", "6720", "6720", "172972800", "1210809600", "7264857600", "36324288000", "145297152000", "435891456000", "871782912000", "871782912000", "1676837160768946176000", "25152557411534192640000", "352135803761478696960000", "4577765448899223060480000" ]
[ "nonn" ]
20
2
1
[ "A006845", "A007041" ]
[ "M2016" ]
N. J. A. Sloane
2017-11-06T02:41:39
oeisdata/seq/A007/A007041.seq
b3f155545e575cf202cf21dbfb4df38f
A007042
Left diagonal of partition triangle A047812.
[ "0", "1", "3", "5", "9", "13", "20", "28", "40", "54", "75", "99", "133", "174", "229", "295", "383", "488", "625", "790", "1000", "1253", "1573", "1956", "2434", "3008", "3716", "4563", "5602", "6840", "8347", "10141", "12308", "14881", "17975", "21635", "26013", "31183", "37336", "44581", "53172", "63259", "75173", "89132", "105556", "124752" ]
[ "nonn", "easy", "nice" ]
59
1
3
[ "A000041", "A007042", "A007044", "A007045", "A026820", "A047812", "A051643", "A081719", "A096651" ]
[ "M2451" ]
N. J. A. Sloane, R. K. Guy
2020-06-01T13:09:34
oeisdata/seq/A007/A007042.seq
59e7f7d70495800778db945c7653ca5d
A007043
Number of noncommutative SL(2,C)-invariants of degree n in 5 variables.
[ "1", "0", "1", "1", "5", "16", "65", "260", "1085", "4600", "19845", "86725", "383251", "1709566", "7687615", "34812519", "158614405", "726612216", "3344696501", "15462729645", "71763732545", "334236300200", "1561686608685", "7318223046860", "34386154568375", "161970182441556", "764676831501575", "3617755131480841" ]
[ "nonn" ]
93
0
5
[ "A000108", "A007043", "A348210" ]
[ "M3870" ]
N. J. A. Sloane and Mira Bernstein
2025-02-17T01:32:53
oeisdata/seq/A007/A007043.seq
d5a69bea1f5842a3c51211ad79ca874d
A007044
Left diagonal of partition triangle A047812.
[ "0", "0", "1", "7", "20", "48", "100", "194", "352", "615", "1034", "1693", "2705", "4239", "6522", "9889", "14786", "21844", "31913", "46165", "66162", "94035", "132600", "185637", "258128", "356674", "489906", "669173", "909212", "1229217", "1653993", "2215597", "2955192", "3925659", "5194520", "6847963", "8995524", "11776227" ]
[ "nonn" ]
34
1
4
[ "A007042", "A007044", "A007045", "A047812", "A051643" ]
[ "M4370" ]
N. J. A. Sloane and R. K. Guy
2020-11-23T06:06:59
oeisdata/seq/A007/A007044.seq
b9f9512218ef6fef087febb61c981e5c
A007045
Second (lower) diagonal of partition triangle A047812.
[ "0", "1", "5", "20", "51", "112", "221", "411", "720", "1221", "2003", "3206", "5021", "7728", "11698", "17472", "25766", "37580", "54254", "77617", "110087", "154942", "216488", "300456", "414365", "568113", "774571", "1050572", "1417868", "1904641", "2547152", "3392042", "4498948", "5944158", "7824703", "10263932", "13418043", "17484554" ]
[ "nonn", "nice" ]
53
2
3
[ "A007042", "A007044", "A007045", "A047812", "A051643" ]
[ "M3896" ]
N. J. A. Sloane and R. K. Guy
2020-05-31T19:40:25
oeisdata/seq/A007/A007045.seq
eb26356fcb257e8c7ce8a6f78a6768a6
A007046
Number of irreducible positions of size n in Montreal solitaire.
[ "1", "3", "9", "25", "70", "194", "537", "1485", "4104", "11338", "31318", "86498", "238885", "659713", "1821843", "5031071", "13893316", "38366206", "105947374", "292570493", "807923428", "2231050832", "6160961041", "17013250192", "46981405457", "129737238488", "358264064448", "989331456469" ]
[ "nonn" ]
17
3
2
[ "A007046", "A007048", "A007049", "A007050", "A007075", "A007076" ]
[ "M2800" ]
N. J. A. Sloane, Mira Bernstein
2017-09-26T02:51:22
oeisdata/seq/A007/A007046.seq
0c0cbca9d6847412e2e9118ce0c01fa2
A007047
Number of chains in power set of n-set.
[ "1", "3", "11", "51", "299", "2163", "18731", "189171", "2183339", "28349043", "408990251", "6490530291", "112366270379", "2107433393523", "42565371881771", "921132763911411", "21262618727925419", "521483068116543603", "13542138653027381291", "371206349277313644531" ]
[ "nonn", "nice", "easy" ]
146
0
2
[ "A000629", "A000670", "A007047", "A038719" ]
[ "M2903" ]
N. J. A. Sloane, Roger B. Nelsen
2024-08-07T09:19:35
oeisdata/seq/A007/A007047.seq
394859ff1e14634e4ebc45a6045e9b3e
A007048
Number of irreducible positions of size n in Montreal solitaire.
[ "1", "2", "4", "11", "28", "77", "209", "573", "1576", "4340", "11964", "33004", "91080", "251407", "694065", "1916306", "5291223", "14610468", "40344380", "111406090", "307637516", "849517917", "2345890032", "6478044971", "17888793238", "49399054113", "136413247359", "376699178348", "1040238528205" ]
[ "nonn" ]
17
1
2
[ "A007046", "A007048", "A007049", "A007050", "A007075", "A007076" ]
[ "M1246" ]
N. J. A. Sloane, Mira Bernstein
2017-09-26T02:51:12
oeisdata/seq/A007/A007048.seq
6dbd42f7d48c9c098ff0b30a91d6e780
A007049
Number of irreducible positions of size n in Montreal solitaire.
[ "1", "2", "7", "17", "49", "134", "368", "1017", "2806", "7743", "21374", "59015", "162942", "449916", "1242352", "3430578", "9473170", "26159353", "72237232", "199478805", "550850090", "1521145442", "4200572421", "11599692758", "32032045540", "88455119858", "244265061492", "674527681575" ]
[ "nonn" ]
17
3
2
[ "A007046", "A007048", "A007049", "A007050", "A007075", "A007076" ]
[ "M1746" ]
N. J. A. Sloane, Mira Bernstein
2017-09-26T02:51:02
oeisdata/seq/A007/A007049.seq
510b91d71f46aa52538774c3330ee85c
A007050
Number of irreducible positions of size n in Montreal solitaire.
[ "1", "2", "7", "21", "57", "162", "452", "1255", "3474", "9621", "26604", "73531", "203166", "561242", "1550216", "4281502", "11824338", "32654467", "90177615", "249028277", "687692923", "1899056307", "5244202459", "14481714130", "39990771798", "110433069740", "304956719409", "842126002534" ]
[ "nonn" ]
17
6
2
[ "A007046", "A007048", "A007049", "A007050", "A007075", "A007076" ]
[ "M1754" ]
N. J. A. Sloane, Mira Bernstein
2017-09-26T02:50:45
oeisdata/seq/A007/A007050.seq
9279ffcf6daad9898d931670a6b99255
A007051
a(n) = (3^n + 1)/2.
[ "1", "2", "5", "14", "41", "122", "365", "1094", "3281", "9842", "29525", "88574", "265721", "797162", "2391485", "7174454", "21523361", "64570082", "193710245", "581130734", "1743392201", "5230176602", "15690529805", "47071589414", "141214768241", "423644304722", "1270932914165", "3812798742494", "11438396227481" ]
[ "easy", "nonn", "nice" ]
354
0
2
[ "A000079", "A000392", "A003462", "A007051", "A007581", "A007583", "A008277", "A034472", "A056272", "A056273", "A056449", "A064881", "A064886", "A065363", "A071919", "A083065", "A083066", "A147292", "A278984" ]
[ "M1458" ]
Colin Mallows, N. J. A. Sloane, Simon Plouffe, Robert G. Wilson v
2025-02-21T12:19:57
oeisdata/seq/A007/A007051.seq
c1ae6e48ca42635ac16a38e822705bb1
A007052
Number of order-consecutive partitions of n.
[ "1", "3", "10", "34", "116", "396", "1352", "4616", "15760", "53808", "183712", "627232", "2141504", "7311552", "24963200", "85229696", "290992384", "993510144", "3392055808", "11581202944", "39540700160", "135000394752", "460920178688", "1573679925248", "5372879343616", "18344157523968", "62630871408640", "213835170586624" ]
[ "nonn", "easy" ]
143
0
2
[ "A000129", "A000670", "A001523", "A001653", "A003480", "A006012", "A007052", "A007068", "A007070", "A035344", "A056236", "A060223", "A075271", "A227038", "A291292", "A328509", "A332577", "A332743", "A332873" ]
[ "M2847" ]
Colin Mallows, N. J. A. Sloane, Simon Plouffe
2024-12-29T14:28:40
oeisdata/seq/A007/A007052.seq
2fc6d14c82dd19ebc12765122bec2577
A007053
Number of primes <= 2^n.
[ "0", "1", "2", "4", "6", "11", "18", "31", "54", "97", "172", "309", "564", "1028", "1900", "3512", "6542", "12251", "23000", "43390", "82025", "155611", "295947", "564163", "1077871", "2063689", "3957809", "7603553", "14630843", "28192750", "54400028", "105097565", "203280221", "393615806", "762939111", "1480206279", "2874398515", "5586502348", "10866266172", "21151907950", "41203088796", "80316571436", "156661034233", "305761713237", "597116381732", "1166746786182", "2280998753949", "4461632979717", "8731188863470", "17094432576778", "33483379603407", "65612899915304", "128625503610475" ]
[ "nonn", "nice" ]
110
0
3
[ "A006880", "A007053", "A036378" ]
[ "M1018" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v, S. W. Golomb
2023-04-03T10:36:09
oeisdata/seq/A007/A007053.seq
141a055a309b383c2159f075c7959929
A007054
Super ballot numbers: 6(2n)!/(n!(n+2)!).
[ "3", "2", "3", "6", "14", "36", "99", "286", "858", "2652", "8398", "27132", "89148", "297160", "1002915", "3421710", "11785890", "40940460", "143291610", "504932340", "1790214660", "6382504440", "22870640910", "82334307276", "297670187844", "1080432533656", "3935861372604", "14386251913656", "52749590350072" ]
[ "nonn", "easy" ]
120
0
1
[ "A000257", "A001622", "A002421", "A007054", "A007272", "A091712" ]
[ "M2243" ]
N. J. A. Sloane, Mira Bernstein, Ira M. Gessel
2025-01-20T10:51:11
oeisdata/seq/A007/A007054.seq
5cf423bcda80994a735d0b3e27a7581e
A007055
Let S denote the palindromes in the language {0,1}*; a(n) = number of words of length n in the language SS.
[ "1", "2", "4", "8", "16", "32", "52", "100", "160", "260", "424", "684", "1036", "1640", "2552", "3728", "5920", "8672", "13408", "19420", "30136", "42736", "66840", "94164", "145900", "204632", "317776", "441764", "685232", "950216", "1469632", "2031556", "3139360", "4323888", "6675904", "9174400", "14139496", "19398584", "29864888", "40891040", "62882680", "85983152" ]
[ "nonn" ]
63
0
2
[ "A006995", "A007055", "A007056", "A007058", "A023900", "A057148", "A187272", "A187275", "A284873" ]
[ "M1124" ]
N. J. A. Sloane, Mira Bernstein, R. Kemp
2024-02-18T22:57:24
oeisdata/seq/A007/A007055.seq
c573ddc7ee099f8f5babcc506af635d6
A007056
Let S denote the palindromes in the language {0,1,2}*; a(n) = number of words of length n in the language SS.
[ "1", "3", "9", "21", "57", "123", "279", "549", "1209", "2127", "4689", "7989", "17031", "28395", "60615", "98061", "208569", "334563", "705789", "1121877", "2356737", "3718827", "7786359", "12223077", "25488903", "39857523", "82876257", "129135729", "267784119", "416118219", "860825439", "1334448261", "2754778809", "4261609131", "8781196329", "13559714109", "27893530029" ]
[ "nonn" ]
27
0
2
[ "A007056", "A284873" ]
[ "M2781" ]
N. J. A. Sloane, Mira Bernstein, R. Kemp
2024-02-19T11:51:43
oeisdata/seq/A007/A007056.seq
c3c54077af1344c8356a485e07e54a6a
A007057
Let S denote the palindromes in the language {0,1,2,3}*; a(n) = number of words of length n in the language SS.
[ "1", "4", "16", "40", "136", "304", "880", "1768", "4936", "9112", "25216", "45016", "121600", "212944", "571552", "982240", "2616136", "4456384", "11785408", "19922872", "52402336", "88076560", "230641504", "385875880", "1006499200", "1677720304", "4361862976", "7247738776", "18789905872", "31138512784", "80529599680", "133143986056", "343594756936" ]
[ "nonn" ]
27
0
2
[ "A007057", "A284873" ]
[ "M3510" ]
N. J. A. Sloane, Mira Bernstein, R. Kemp
2024-02-19T11:49:56
oeisdata/seq/A007/A007057.seq
2dcc72be3a58661921bcf9a99381eae5
A007058
Let S denote the palindromes in the language {0,1,2,3,4}*; a(n) = number of words of length n in the language SS.
[ "1", "5", "25", "65", "265", "605", "2125", "4345", "14665", "27965", "93025", "171825", "559645", "1015565", "3276725", "5857865", "18734665", "33203045", "105436225", "185546785", "585842065", "1025381485", "3222484125", "5615234265", "17577530845", "30517575605", "95213827825", "164794865465", "512692025285", "885009765485", "2746575977125" ]
[ "nonn" ]
28
0
2
[ "A007055", "A007056", "A007057", "A007058", "A284873" ]
[ "M3936" ]
N. J. A. Sloane, Mira Bernstein, R. Kemp
2024-02-19T11:51:48
oeisdata/seq/A007/A007058.seq
57d4537a4b029e7c3e7d15a0cd0e0895
A007059
Number of balanced ordered trees with n nodes.
[ "0", "1", "1", "2", "3", "5", "8", "14", "24", "43", "77", "140", "256", "472", "874", "1628", "3045", "5719", "10780", "20388", "38674", "73562", "140268", "268066", "513350", "984911", "1892875", "3643570", "7023562", "13557020", "26200182", "50691978", "98182666", "190353370", "369393466", "717457656" ]
[ "nonn", "nice", "easy" ]
65
0
4
[ "A007059", "A048888", "A092921" ]
[ "M0699" ]
N. J. A. Sloane, Mira Bernstein, R. Kemp
2024-01-05T10:13:59
oeisdata/seq/A007/A007059.seq
b4c9bf00f97d35788da94334f385120f
A007060
Number of ways n married couples can sit in a row without any spouses next to each other.
[ "1", "0", "8", "240", "13824", "1263360", "168422400", "30865121280", "7445355724800", "2287168006717440", "871804170613555200", "403779880746418176000", "223346806774106790297600", "145427383048755178635264000", "110105698060190464791596236800", "95914116314126658718742347776000", "95252504853751428295192341381120000" ]
[ "nonn", "easy", "nice" ]
78
0
3
[ "A000166", "A000806", "A007060", "A053983", "A053984", "A114938", "A177840", "A193624", "A229430", "A330266" ]
null
David Roberts Keeney (David.Roberts.Keeney(AT)directory.Reed.edu)
2025-02-16T08:32:31
oeisdata/seq/A007/A007060.seq
d7598b6c51d41ba76f03e175bb9baa3f
A007061
The Ehrenfeucht-Mycielski sequence (1,2-version): a maximally unpredictable sequence.
[ "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "2", "2", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "1", "1", "2", "1", "1", "2", "2", "2", "1", "2", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "1", "2", "2", "1", "2", "2", "2", "2", "2", "1", "1", "2", "2", "1", "1", "2", "2", "2", "2", "2", "2", "1", "2", "1", "2", "1", "2", "2", "1", "1", "1", "2", "2", "2", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "2" ]
[ "nonn" ]
50
1
2
[ "A007061", "A038219", "A079101", "A201881", "A253059", "A253060", "A253061" ]
[ "M0075" ]
N. J. A. Sloane, Mira Bernstein
2024-01-29T01:53:38
oeisdata/seq/A007/A007061.seq
c16d2a9ffc15ad34f70163158463ce0f
A007062
Let P(n) of a sequence s(1),s(2),s(3),... be obtained by leaving s(1),...,s(n) fixed and reversing every n consecutive terms thereafter; apply P(2) to 1,2,3,... to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. This sequence is the limit of PS(n).
[ "1", "2", "4", "5", "7", "12", "14", "15", "23", "28", "30", "41", "43", "48", "56", "67", "69", "84", "86", "87", "111", "116", "124", "139", "141", "162", "180", "181", "183", "224", "232", "237", "271", "276", "278", "315", "333", "338", "372", "383", "385", "426", "428", "439", "473", "478", "538", "543", "551", "556", "620" ]
[ "nonn" ]
48
1
2
[ "A007062", "A057030", "A057032", "A057033", "A057063", "A057064" ]
[ "M0966" ]
N. J. A. Sloane, Mira Bernstein
2024-04-24T08:21:12
oeisdata/seq/A007/A007062.seq
bdbae225d771885b20c0a46d269e61d4
A007063
Main diagonal of Kimberling's expulsion array (A035486).
[ "1", "3", "5", "4", "10", "7", "15", "8", "20", "9", "18", "24", "31", "14", "28", "22", "42", "35", "33", "46", "53", "6", "36", "23", "2", "55", "62", "59", "76", "65", "54", "11", "34", "48", "70", "79", "99", "95", "44", "97", "58", "84", "25", "13", "122", "83", "26", "115", "82", "91", "52", "138", "67", "90", "71", "119", "64", "37", "81", "39", "169", "88", "108", "141", "38", "16", "146", "41", "21" ]
[ "nonn", "nice", "easy" ]
79
1
2
[ "A006852", "A007063", "A035486", "A038807", "A175312", "A282348", "A356026", "A356376", "A356377", "A356378", "A356379", "A356380" ]
[ "M2387" ]
N. J. A. Sloane, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007063.seq
d2208e50b174c180a4b2ba1992eacb45
A007064
Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2.
[ "1", "4", "7", "9", "12", "14", "17", "20", "22", "25", "27", "30", "33", "35", "38", "41", "43", "46", "48", "51", "54", "56", "59", "62", "64", "67", "69", "72", "75", "77", "80", "82", "85", "88", "90", "93", "96", "98", "101", "103", "106", "109", "111", "114", "117", "119", "122", "124", "127", "130", "132", "135" ]
[ "nonn", "easy", "nice" ]
46
1
2
[ "A001622", "A007064", "A007067", "A035506" ]
[ "M3298" ]
N. J. A. Sloane, Mira Bernstein
2025-02-12T09:31:31
oeisdata/seq/A007/A007064.seq
ff62603f71736ceb19cb428c80f7cdba
A007065
Number of M-sequences from multicomplexes on at most 5 variables with no monomial of degree greater than n.
[ "1", "2", "7", "42", "392", "5345", "102050", "2632429", "89026966", "3851458088", "208865852153", "13957985705937", "1132644571676551", "110180310623136151", "12704646305768038117", "1719311705781104612966" ]
[ "nonn" ]
7
-1
2
[ "A003659", "A007065", "A011819", "A011820" ]
null
N. J. A. Sloane.
2012-03-30T16:45:07
oeisdata/seq/A007/A007065.seq
87a194aba5fccd46a2dcae7fc993ad4a
A007066
a(n) = 1 + ceiling((n-1)*phi^2), phi = (1+sqrt(5))/2.
[ "1", "4", "7", "9", "12", "15", "17", "20", "22", "25", "28", "30", "33", "36", "38", "41", "43", "46", "49", "51", "54", "56", "59", "62", "64", "67", "70", "72", "75", "77", "80", "83", "85", "88", "91", "93", "96", "98", "101", "104", "106", "109", "111", "114", "117", "119", "122", "125", "127", "130", "132", "135", "138", "140", "143", "145", "148", "151", "153", "156", "159", "161", "164", "166" ]
[ "nonn", "easy", "nice" ]
57
1
2
[ "A001950", "A004956", "A004957", "A007066", "A026355", "A026356", "A064437", "A076662", "A099267", "A193214" ]
[ "M3299" ]
N. J. A. Sloane, Mira Bernstein
2022-08-26T10:26:36
oeisdata/seq/A007/A007066.seq
661fc04181204d2de1ed8bd9f91bf76f
A007067
Nearest integer to n*tau where tau = (1+sqrt(5))/2.
[ "0", "2", "3", "5", "6", "8", "10", "11", "13", "15", "16", "18", "19", "21", "23", "24", "26", "28", "29", "31", "32", "34", "36", "37", "39", "40", "42", "44", "45", "47", "49", "50", "52", "53", "55", "57", "58", "60", "61", "63", "65", "66", "68", "70", "71", "73", "74", "76", "78", "79", "81", "83", "84", "86", "87", "89", "91", "92", "94", "95", "97", "99", "100", "102", "104", "105" ]
[ "nonn", "easy" ]
64
0
2
[ "A000045", "A000201", "A001622", "A004956", "A007064", "A007067", "A022342", "A026355", "A066096", "A166946", "A295282" ]
[ "M0622" ]
N. J. A. Sloane, Mira Bernstein
2024-02-14T17:31:24
oeisdata/seq/A007/A007067.seq
6f9e6ab9f3ce5de3cece71fa0db991b2
A007068
a(n) = a(n-1) + (3+(-1)^n)*a(n-2)/2.
[ "1", "3", "4", "10", "14", "34", "48", "116", "164", "396", "560", "1352", "1912", "4616", "6528", "15760", "22288", "53808", "76096", "183712", "259808", "627232", "887040", "2141504", "3028544", "7311552", "10340096", "24963200", "35303296", "85229696", "120532992", "290992384", "411525376" ]
[ "nonn", "easy", "nice" ]
54
1
2
[ "A000034", "A001882", "A007052", "A007068", "A007070", "A062112" ]
[ "M2360" ]
N. J. A. Sloane, Mira Bernstein
2024-08-03T02:29:53
oeisdata/seq/A007/A007068.seq
e39f4352d15a3745f4c193cc6cb5f6cb
A007069
First column of spectral array W(sqrt 2).
[ "1", "2", "5", "7", "9", "11", "12", "15", "16", "19", "21", "22", "25", "26", "29", "31", "33", "35", "36", "39", "41", "43", "45", "46", "49", "50", "53", "55", "57", "59", "60", "63", "65", "67", "69", "70", "73", "74", "77", "79", "80", "83", "84", "87", "89", "91", "93", "94", "97", "98", "101", "103", "104", "107", "108", "111", "113", "115", "117", "118", "121", "123", "125", "127", "128", "131" ]
[ "nonn" ]
34
1
2
[ "A001951", "A007069", "A059648" ]
[ "M1329" ]
N. J. A. Sloane, Mira Bernstein
2022-08-30T02:11:18
oeisdata/seq/A007/A007069.seq
d8af0aa6d71ecd15ce432ef1e2ee9b8b
A007070
a(n) = 4*a(n-1) - 2*a(n-2) with a(0) = 1, a(1) = 4.
[ "1", "4", "14", "48", "164", "560", "1912", "6528", "22288", "76096", "259808", "887040", "3028544", "10340096", "35303296", "120532992", "411525376", "1405035520", "4797091328", "16378294272", "55918994432", "190919389184", "651839567872", "2225519493120", "7598398836736", "25942556360704", "88573427769344", "302408598355968" ]
[ "nonn", "easy" ]
202
0
2
[ "A000129", "A000225", "A002307", "A002315", "A003480", "A006012", "A007052", "A007070", "A059474", "A075271", "A078057", "A106731", "A127672", "A133314", "A140071", "A179260", "A204089", "A228405", "A265185" ]
[ "M3482" ]
N. J. A. Sloane, Mira Bernstein, Simon Plouffe
2025-04-12T10:28:13
oeisdata/seq/A007/A007070.seq
97b4ef2352cdbe9b9dba07b4c7ea594c
A007071
First row of 2-shuffle of spectral array W( sqrt 2 ).
[ "1", "2", "3", "5", "6", "7", "9", "11", "12", "13", "15", "16", "17", "19", "21", "22", "23", "25", "26", "27", "29", "30", "31", "33", "35", "36", "37", "39", "40", "41", "43", "45", "46", "47", "49", "50", "51", "53", "54", "55", "57", "59", "60", "61", "63", "64", "65", "67", "69", "70", "71", "73", "74", "75", "77", "79", "80", "81", "83", "84", "85", "87", "88", "89", "91", "93", "94", "95", "97", "98", "99", "101" ]
[ "nonn", "easy" ]
22
1
2
null
[ "M0616" ]
N. J. A. Sloane, Mira Bernstein
2023-12-21T10:23:23
oeisdata/seq/A007/A007071.seq
c65cade2f13da6cd1854f29227bab43e
A007072
First column of array associated with monotonic justified array.
[ "1", "4", "7", "9", "12", "14", "17", "19", "22", "25", "27", "30", "33", "35", "38", "41", "43", "46", "49", "51", "54", "57", "59", "62", "64", "67", "70", "72", "75", "77", "80", "83", "85", "88", "90", "93", "96", "98", "101", "103", "106", "109", "111", "113", "114", "116", "119", "121", "122", "124", "127", "129", "132", "134", "135", "137", "140" ]
[ "nonn" ]
20
1
2
null
[ "M3297" ]
N. J. A. Sloane, Mira Bernstein
2017-10-06T01:43:45
oeisdata/seq/A007/A007072.seq
aa317def11d1b50e2d825b0ca4478eab
A007073
First column of array associated with lexicographically justified array.
[ "1", "4", "7", "9", "12", "14", "17", "20", "22", "25", "27", "30", "33", "35", "38", "41", "43", "46", "48", "51", "54", "56", "59", "62", "64", "67", "69", "72", "75", "77", "80", "83", "85", "88", "90", "93", "96", "98", "101", "103", "106", "109", "111", "114", "117", "119", "122", "124", "127", "130", "132", "135", "137", "140", "143", "145", "148" ]
[ "nonn" ]
24
1
2
[ "A007064", "A007073" ]
[ "M3279" ]
N. J. A. Sloane, Mira Bernstein
2017-10-06T17:32:37
oeisdata/seq/A007/A007073.seq
12a2f1b3b4ea5ef41ac1e4ea72034296
A007074
First column of array associated with reverse lexicographically justified array.
[ "1", "4", "6", "9", "12", "15", "17", "20", "22", "25", "28", "30", "33", "35", "38", "40", "43", "46", "48", "51", "54", "56", "59", "61", "64", "67", "69", "72", "75", "77", "80", "82", "85", "88", "90", "93", "96", "98", "101", "104", "106", "109", "111", "114", "117", "119", "122", "124", "127", "130", "132", "135", "138", "140", "143", "145", "148" ]
[ "nonn" ]
22
1
2
null
[ "M3280" ]
N. J. A. Sloane, Mira Bernstein
2019-03-17T12:46:44
oeisdata/seq/A007/A007074.seq
ac52091b762ecb75db22b3a8639a4c8e
A007075
Number of irreducible positions of size n in Montreal solitaire.
[ "1", "2", "5", "13", "35", "95", "260", "714", "1965", "5415", "14934", "41206", "113730", "313958", "866801", "2393315", "6608473", "18248017", "50389350", "139144906", "384237186", "1061044865", "2930013158", "8091077148", "22343115337", "61699480866", "170380367189", "470497972866" ]
[ "nonn" ]
33
1
2
[ "A007046", "A007048", "A007049", "A007050", "A007075", "A007076" ]
[ "M1441" ]
N. J. A. Sloane, Mira Bernstein
2017-12-20T04:12:10
oeisdata/seq/A007/A007075.seq
8d1ab549ca8fc971636719385502d640
A007076
Number of irreducible positions of size n in Montreal solitaire.
[ "1", "4", "14", "42", "123", "351", "988", "2761", "7682", "21313", "59029", "163314", "451529", "1247842", "3447574", "9523375", "26303825", "72646588", "200627795", "554056162", "1530058222", "4225290890", "11668141901", "32221405479", "88978639438", "245711832196", "678524838258" ]
[ "nonn" ]
19
6
2
[ "A007046", "A007048", "A007049", "A007050", "A007075", "A007076" ]
[ "M3477" ]
N. J. A. Sloane, Mira Bernstein
2017-10-06T17:32:14
oeisdata/seq/A007/A007076.seq
2fa02215116339a43864c35f102eb4d9
A007077
Optimal cost of search tree for searching an ordered array of n elements with cost k of probing element k.
[ "1", "4", "10", "19", "31", "47", "68", "92", "120", "153", "190", "232", "279", "332", "392", "454", "521", "593", "670", "753", "841", "936", "1036", "1141", "1252", "1370", "1494", "1625", "1763", "1909", "2063", "2216", "2376", "2542", "2713", "2890", "3074", "3264", "3460", "3663", "3872", "4088", "4310", "4540", "4776", "5021" ]
[ "nonn" ]
32
1
2
[ "A007077", "A007078" ]
[ "M3379" ]
N. J. A. Sloane, Mira Bernstein
2017-11-16T06:19:38
oeisdata/seq/A007/A007077.seq
9d98518dc94cbda4cf509a8f2f307212
A007078
Optimal cost of search tree.
[ "1", "3", "5", "7", "9", "12", "15", "19", "23", "26", "29", "32", "35", "38", "41", "45", "49", "53", "57", "62", "67", "72", "77", "83", "89", "93", "97", "101", "105", "109", "113", "117", "121", "125", "129", "133", "137", "141", "145", "150", "155", "160", "165", "170", "175", "180", "185", "191", "197", "203", "209", "215", "221" ]
[ "nonn" ]
24
1
2
[ "A007077", "A007078" ]
[ "M2402" ]
N. J. A. Sloane, Mira Bernstein
2017-11-16T06:19:48
oeisdata/seq/A007/A007078.seq
091f3fc97f92993c794ca02073162c9d
A007079
Number of labeled regular tournaments with 2n+1 nodes.
[ "1", "2", "24", "2640", "3230080", "48251508480", "9307700611292160", "24061983498249428379648", "855847205541481495117975879680", "427102683126284520201657800159366676480", "3035991776725501434069099002640396043332019814400", "311112533558482034321687955029997989477274014274150137856000" ]
[ "nonn", "nice" ]
36
0
2
null
[ "M2142" ]
N. J. A. Sloane, Mira Bernstein
2023-09-30T18:49:40
oeisdata/seq/A007/A007079.seq
4c25cfae57064f88219dcdea743f0ff4
A007080
Number of labeled Eulerian digraphs with n nodes.
[ "1", "2", "10", "152", "7736", "1375952", "877901648", "2046320373120", "17658221702361472", "569773219836965265152", "69280070663388783890248448", "31941407692847758201303724506112", "56121720938871110502272391300032261120", "377362438996731353329256282026362716827887616", "9744754031799754169218003376206941877943086188308480", "969342741943194323476512925742876053501022995325734477987840" ]
[ "nonn", "nice" ]
69
1
2
[ "A007080", "A054957", "A058338", "A229865" ]
[ "M1989" ]
N. J. A. Sloane, Mira Bernstein
2025-03-20T04:17:39
oeisdata/seq/A007/A007080.seq
4f88fafce09826b8a16d6dd1a1a09fa3
A007081
Number of labeled Eulerian oriented graphs with n nodes.
[ "1", "1", "3", "15", "219", "7839", "777069", "208836207", "156458382975", "328208016021561", "1946879656265710431", "32834193098697741359313", "1582809785794578499063205301", "218989607557709869788340418432175", "87269441106898007902526099850864517077" ]
[ "nonn", "nice" ]
20
1
3
null
[ "M3009" ]
N. J. A. Sloane, Mira Bernstein
2017-10-08T18:48:45
oeisdata/seq/A007/A007081.seq
adb1a2b5b54cce6e8a9d7d4de9922320
A007082
Number of Eulerian circuits on the complete graph K_{2n+1}, divided by (n-1)!^(2n+1).
[ "2", "264", "1015440", "90449251200", "169107043478365440", "6267416821165079203599360", "4435711276305905572695127676467200", "58393052751308545653929138771580386824519680", "14021772793551297695593332913856884153315254190271692800", "60498832138791357698014788383803842810832836262245623803123983974400" ]
[ "nonn", "nice", "walk" ]
44
1
1
[ "A007082", "A135388", "A232545", "A350028", "A356366", "A357855", "A357856", "A357857", "A357885", "A357886", "A357887" ]
[ "M2183" ]
N. J. A. Sloane, Mira Bernstein
2022-10-19T11:24:45
oeisdata/seq/A007/A007082.seq
3762b537537e0e6b3d950d745e4d143c
A007083
Number of unlabeled trivalent 3-connected bipartite planar graphs with 2n nodes.
[ "0", "0", "1", "0", "1", "1", "2", "2", "8", "8", "32", "57", "185", "466", "1543", "4583", "15374", "50116", "171168", "582603", "2024119", "7057472", "24873248", "88111772", "314301078", "1126716000", "4060375677", "14697571234", "53432834170", "195015189626", "714404259151", "2626130395699" ]
[ "nonn" ]
32
2
7
[ "A007083", "A169955" ]
[ "M0372" ]
N. J. A. Sloane, Mira Bernstein
2019-09-20T04:44:42
oeisdata/seq/A007/A007083.seq
ca63a8b4608c7444d731b85db7f1db17
A007084
Number of unlabeled trivalent 3-connected bipartite planar graphs with 2n nodes without subgraphs R2 and R4.
[ "0", "0", "0", "0", "1", "1", "1", "4", "5", "14", "28", "86", "211", "648", "1878", "5931", "18326", "58746", "187620", "608065", "1975191", "6461809", "21212414" ]
[ "nonn", "more" ]
22
2
8
[ "A007083", "A007084" ]
[ "M3255" ]
N. J. A. Sloane, Mira Bernstein
2017-10-09T02:31:07
oeisdata/seq/A007/A007084.seq
e3aad0d285a9331c0022744735181169
A007085
Number of unlabeled trivalent 3-connected bipartite planar graphs with 2n nodes without subgraphs R1 and R4.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "3", "1", "5", "4", "11", "20", "46", "89", "243", "525", "1359", "3316" ]
[ "nonn", "more" ]
17
2
12
[ "A007083", "A007085" ]
[ "M2224" ]
N. J. A. Sloane, Mira Bernstein
2017-10-09T02:17:02
oeisdata/seq/A007/A007085.seq
52d60f19dedb4747302650dc71aabbf6
A007086
Next term is uniquely the sum of 3 earlier terms.
[ "1", "2", "3", "6", "9", "10", "11", "12", "28", "29", "30", "53", "56", "57", "80", "82", "104", "105", "107", "129", "130", "132", "154", "155", "157", "179", "180", "182", "204", "205", "207", "229", "230", "232", "254", "255", "257", "279", "280", "282", "304", "305", "307", "329", "330", "332", "354", "355", "357", "379", "380", "382", "404", "405", "407", "429" ]
[ "nonn" ]
26
1
2
[ "A002858", "A007086" ]
[ "M0756" ]
N. J. A. Sloane, Robert G. Wilson v
2017-11-07T18:20:28
oeisdata/seq/A007/A007086.seq
dd09d3b2cb2a5f1ded2bb7811edc4c43
A007087
Next term is uniquely the sum of 3 earlier terms.
[ "1", "2", "4", "7", "10", "12", "16", "17", "32", "36", "42", "57", "72", "73", "98", "102", "104", "129", "159", "164", "174", "189", "199", "221", "224", "255", "286", "287", "347", "372", "378", "403", "428", "443", "444", "469", "494", "529", "560", "586" ]
[ "nonn" ]
13
1
2
null
[ "M1035" ]
N. J. A. Sloane, Robert G. Wilson v
2017-11-07T18:20:36
oeisdata/seq/A007/A007087.seq
343cbe8efdd9ebd820c2e3e07c485185
A007088
The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2.
[ "0", "1", "10", "11", "100", "101", "110", "111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111", "10000", "10001", "10010", "10011", "10100", "10101", "10110", "10111", "11000", "11001", "11010", "11011", "11100", "11101", "11110", "11111", "100000", "100001", "100010", "100011", "100100", "100101", "100110", "100111" ]
[ "nonn", "base", "nice", "easy" ]
176
0
3
[ "A000042", "A000069", "A000120", "A000290", "A000695", "A000788", "A001737", "A001969", "A004290", "A005836", "A007088", "A007089", "A007095", "A007953", "A023416", "A028897", "A030308", "A033042", "A033052", "A054055", "A059015", "A064770", "A097256", "A099820", "A099821", "A101337", "A136399", "A159918", "A169964", "A169965", "A169966", "A169967", "A204093", "A204094", "A204095", "A257770", "A257773" ]
[ "M4679" ]
N. J. A. Sloane, Robert G. Wilson v
2025-03-07T07:50:11
oeisdata/seq/A007/A007088.seq
0f02400b69b457e263125d6f8640ae5f
A007089
Numbers in base 3.
[ "0", "1", "2", "10", "11", "12", "20", "21", "22", "100", "101", "102", "110", "111", "112", "120", "121", "122", "200", "201", "202", "210", "211", "212", "220", "221", "222", "1000", "1001", "1002", "1010", "1011", "1012", "1020", "1021", "1022", "1100", "1101", "1102", "1110", "1111", "1112", "1120", "1121", "1122", "1200", "1201", "1202", "1210", "1211" ]
[ "base", "nonn", "easy" ]
65
0
3
[ "A000042", "A003137", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095", "A036954", "A054635", "A062756", "A077267", "A081603", "A081604" ]
[ "M1960" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007089.seq
959fbb401cb17c0606bba2edf61336ba
A007090
Numbers in base 4.
[ "0", "1", "2", "3", "10", "11", "12", "13", "20", "21", "22", "23", "30", "31", "32", "33", "100", "101", "102", "103", "110", "111", "112", "113", "120", "121", "122", "123", "130", "131", "132", "133", "200", "201", "202", "203", "210", "211", "212", "213", "220", "221", "222", "223", "230", "231", "232", "233", "300", "301", "302", "303", "310", "311", "312", "313", "320", "321", "322", "323", "330", "331", "332", "333" ]
[ "nonn", "easy", "base" ]
65
0
3
[ "A000042", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095", "A007608", "A107715", "A193890" ]
[ "M0900" ]
N. J. A. Sloane, Robert G. Wilson v
2022-12-07T09:46:35
oeisdata/seq/A007/A007090.seq
d74b283c2a2bd74400258438e7597ccd
A007091
Numbers in base 5.
[ "0", "1", "2", "3", "4", "10", "11", "12", "13", "14", "20", "21", "22", "23", "24", "30", "31", "32", "33", "34", "40", "41", "42", "43", "44", "100", "101", "102", "103", "104", "110", "111", "112", "113", "114", "120", "121", "122", "123", "124", "130", "131", "132", "133", "134", "140", "141", "142", "143", "144", "200", "201", "202", "203", "204", "210", "211", "212", "213", "214", "220", "221", "222", "223", "224", "230" ]
[ "nonn", "easy", "base" ]
49
0
3
[ "A000042", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095", "A037454", "A037462", "A102491" ]
[ "M0595" ]
N. J. A. Sloane, Robert G. Wilson v
2021-12-26T14:15:04
oeisdata/seq/A007/A007091.seq
48d13f48d991cd324a39c471fe3e6be1
A007092
Numbers in base 6.
[ "0", "1", "2", "3", "4", "5", "10", "11", "12", "13", "14", "15", "20", "21", "22", "23", "24", "25", "30", "31", "32", "33", "34", "35", "40", "41", "42", "43", "44", "45", "50", "51", "52", "53", "54", "55", "100", "101", "102", "103", "104", "105", "110", "111", "112", "113", "114", "115", "120", "121", "122", "123", "124", "125", "130", "131", "132", "133", "134", "135", "140", "141", "142", "143", "144", "145" ]
[ "nonn", "easy", "base" ]
40
0
3
[ "A000042", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095" ]
[ "M0532" ]
N. J. A. Sloane, Robert G. Wilson v
2019-11-18T22:06:08
oeisdata/seq/A007/A007092.seq
d0212da3372268ba37063347ddebcd70
A007093
Numbers in base 7.
[ "0", "1", "2", "3", "4", "5", "6", "10", "11", "12", "13", "14", "15", "16", "20", "21", "22", "23", "24", "25", "26", "30", "31", "32", "33", "34", "35", "36", "40", "41", "42", "43", "44", "45", "46", "50", "51", "52", "53", "54", "55", "56", "60", "61", "62", "63", "64", "65", "66", "100", "101", "102", "103", "104", "105", "106", "110", "111", "112", "113", "114", "115", "116", "120" ]
[ "nonn", "easy", "base" ]
36
0
3
[ "A000042", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095" ]
[ "M0511" ]
N. J. A. Sloane, Robert G. Wilson v
2024-08-01T01:16:08
oeisdata/seq/A007/A007093.seq
45841fd2ab349943c8346093ff459c2e
A007094
Numbers in base 8.
[ "0", "1", "2", "3", "4", "5", "6", "7", "10", "11", "12", "13", "14", "15", "16", "17", "20", "21", "22", "23", "24", "25", "26", "27", "30", "31", "32", "33", "34", "35", "36", "37", "40", "41", "42", "43", "44", "45", "46", "47", "50", "51", "52", "53", "54", "55", "56", "57", "60", "61", "62", "63", "64", "65", "66", "67", "70", "71", "72", "73", "74", "75", "76", "77", "100", "101", "102", "103", "104", "105", "106", "107", "110", "111" ]
[ "nonn", "easy", "base" ]
61
0
3
[ "A000042", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095", "A057104" ]
[ "M0498" ]
N. J. A. Sloane, Robert G. Wilson v
2025-01-11T02:38:47
oeisdata/seq/A007/A007094.seq
1b89ec643e37222329e3e70ce2cc768b
A007095
Numbers in base 9.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "11", "12", "13", "14", "15", "16", "17", "18", "20", "21", "22", "23", "24", "25", "26", "27", "28", "30", "31", "32", "33", "34", "35", "36", "37", "38", "40", "41", "42", "43", "44", "45", "46", "47", "48", "50", "51", "52", "53", "54", "55", "56", "57", "58", "60", "61", "62", "63", "64", "65", "66", "67", "68", "70", "71", "72", "73", "74", "75", "76", "77", "78", "80", "81", "82", "83", "84" ]
[ "nonn", "easy", "base" ]
70
0
3
[ "A000042", "A007088", "A007089", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095", "A031076", "A031087", "A037479", "A052382", "A052383", "A052404", "A052405", "A052406", "A052413", "A052414", "A052419", "A052421", "A057104", "A082838" ]
[ "M0490" ]
N. J. A. Sloane, Robert G. Wilson v
2022-09-08T08:44:35
oeisdata/seq/A007/A007095.seq
58a03cff416beb9d866f3a967f3a6ef8
A007096
Expansion of theta_3 / theta_4.
[ "1", "4", "8", "16", "32", "56", "96", "160", "256", "404", "624", "944", "1408", "2072", "3008", "4320", "6144", "8648", "12072", "16720", "22976", "31360", "42528", "57312", "76800", "102364", "135728", "179104", "235264", "307672", "400704", "519808", "671744", "864960", "1109904", "1419456", "1809568", "2299832" ]
[ "nonn", "easy" ]
71
0
2
[ "A001936", "A001938", "A007096", "A014969", "A022577", "A079006", "A080054", "A097243", "A123655", "A127391", "A127392" ]
[ "M3332" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:31
oeisdata/seq/A007/A007096.seq
17b080268f9a7c67996f82a0721deda4
A007097
Primeth recurrence: a(n+1) = a(n)-th prime.
[ "1", "2", "3", "5", "11", "31", "127", "709", "5381", "52711", "648391", "9737333", "174440041", "3657500101", "88362852307", "2428095424619", "75063692618249", "2586559730396077", "98552043847093519", "4123221751654370051", "188272405179937051081", "9332039515881088707361", "499720579610303128776791", "28785866289100396890228041" ]
[ "nonn", "hard", "nice" ]
208
0
2
[ "A000040", "A000720", "A006450", "A007097", "A049076", "A049081", "A049084", "A057450", "A078442", "A109082", "A109301", "A114537", "A131842", "A227413", "A245823", "A246378", "A292667" ]
[ "M0734" ]
N. J. A. Sloane, Robert G. Wilson v
2023-01-31T09:34:20
oeisdata/seq/A007/A007097.seq
22acf08635296ff51c98a92cdbd7bc60
A007098
Number of unlabeled bisectable trees with 2n+1 nodes.
[ "1", "1", "3", "6", "19", "47", "140", "374", "1082", "2998", "8574", "24130", "68876", "195587", "559076", "1596651", "4575978", "13122219", "37711998", "108488765", "312577827", "901531937", "2603264050", "7524331268", "21768850808", "63032844756", "182662328945", "529722408615", "1537261773438" ]
[ "nonn" ]
17
0
3
[ "A007098", "A228601" ]
[ "M2596" ]
N. J. A. Sloane, Mira Bernstein
2017-10-11T05:23:12
oeisdata/seq/A007/A007098.seq
6b448de8aba2471e58f07b1d099844ba
A007099
Number of labeled trivalent (or cubic) 2-connected graphs with 2n nodes.
[ "0", "1", "70", "19320", "11052720", "11408720400", "19285018552800", "49792044478176000", "186348919238786304000", "970566620767088881536000", "6808941648018137282054400000", "62642603299257346706851910400000" ]
[ "nonn" ]
28
1
3
[ "A002829", "A004109", "A007099" ]
[ "M5344" ]
N. J. A. Sloane
2021-12-26T21:38:25
oeisdata/seq/A007/A007099.seq
5d478f80f1c65025523afa924e9fe863
A007100
Number of labeled trivalent (or cubic) 3-connected graphs with 2n nodes.
[ "1", "70", "16800", "9238320", "9520156800", "16305064776000", "42856575521760000", "163329351308323200000", "864876880105205071104000", "6155146233167046820024320000", "57316399761348433188962519040000" ]
[ "nonn" ]
14
2
2
null
[ "M5343" ]
N. J. A. Sloane.
2018-03-16T20:12:09
oeisdata/seq/A007/A007100.seq
ea3a1a95ceb1a8526aa567792596ed46