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christopher
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oeis

Dataset card Data Studio Files
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348
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int64
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666,262,453B
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timestamp
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A006601
Numbers k such that k, k+1, k+2 and k+3 have the same number of divisors.
[ "242", "3655", "4503", "5943", "6853", "7256", "8392", "9367", "10983", "11605", "11606", "12565", "12855", "12856", "12872", "13255", "13782", "13783", "14312", "16133", "17095", "18469", "19045", "19142", "19143", "19940", "20165", "20965", "21368", "21494", "21495", "21512", "22855", "23989", "26885" ]
[ "nonn", "easy", "nice" ]
53
1
1
[ "A000005", "A005237", "A005238", "A006558", "A006601", "A019273", "A049051", "A049052", "A049053", "A119479" ]
[ "M5420" ]
N. J. A. Sloane
2024-04-11T04:01:13
oeisdata/seq/A006/A006601.seq
bc3e838d31f333d9955a9967f6b737bd
A006602
a(n) is the number of hierarchical models on n unlabeled factors or variables with linear terms forced.
[ "2", "1", "2", "5", "20", "180", "16143", "489996795", "1392195548399980210", "789204635842035039135545297410259322" ]
[ "nonn", "nice", "hard" ]
68
0
1
[ "A000372", "A003182", "A006126", "A006602", "A007411", "A014466", "A261005", "A293993", "A304997", "A304998", "A304999", "A305001", "A305855", "A306505", "A320449", "A321679" ]
[ "M1532" ]
Colin Mallows
2023-11-27T10:30:11
oeisdata/seq/A006/A006602.seq
4b30f1363db7f9ece22e16214667a59d
A006603
Generalized Fibonacci numbers.
[ "1", "2", "7", "26", "107", "468", "2141", "10124", "49101", "242934", "1221427", "6222838", "32056215", "166690696", "873798681", "4612654808", "24499322137", "130830894666", "702037771647", "3783431872018", "20469182526595", "111133368084892", "605312629105205", "3306633429423460", "18111655081108453" ]
[ "nonn", "easy" ]
34
0
2
[ "A006318", "A006603", "A033877", "A080244", "A180662", "A227504", "A227505" ]
[ "M1771" ]
N. J. A. Sloane, Simon Plouffe
2024-10-28T04:52:45
oeisdata/seq/A006/A006603.seq
4ea3e44de561f7f517347db74db2d649
A006604
Generalized Fibonacci numbers.
[ "1", "1", "4", "13", "53", "228", "1037", "4885", "23640", "116793", "586633", "2986616", "15377097", "79927913", "418852716", "2210503285", "11738292397", "62673984492", "336260313765", "1811960161517", "9802082905840", "53213718977777", "289817858570513", "1583076422786096", "8670574105626961" ]
[ "nonn" ]
33
0
3
null
[ "M3469" ]
N. J. A. Sloane
2025-01-10T12:24:31
oeisdata/seq/A006/A006604.seq
5f333203988b9497646c0f0919f7933c
A006605
Number of modes of connections of 2n points.
[ "1", "1", "3", "11", "46", "207", "979", "4797", "24138", "123998", "647615", "3428493", "18356714", "99229015", "540807165", "2968468275", "16395456762", "91053897066", "508151297602", "2848290555562", "16028132445156", "90516256568235", "512831902620465", "2914112388802779", "16604034506299314" ]
[ "nonn" ]
83
0
3
[ "A001006", "A006605", "A143926" ]
[ "M2899" ]
N. J. A. Sloane
2025-01-08T13:10:17
oeisdata/seq/A006/A006605.seq
287708cc4bf4577ef696afbb6832309e
A006606
Nonperiodic autocorrelation functions of length n.
[ "1", "2", "3", "6", "10", "20", "36", "72", "135", "272", "528", "1048", "2080", "4160", "8242", "16500", "32895", "65750", "131328", "262612", "524733", "1049600", "2098176", "4195930", "8390620", "16781312", "33558177", "67116876", "134225920", "268450626", "536887270" ]
[ "nonn" ]
27
1
2
null
[ "M0770" ]
N. J. A. Sloane
2024-04-25T11:16:35
oeisdata/seq/A006/A006606.seq
240719c087d22f7f2933eb5bae97bbba
A006607
Number of labeled connected rooted trivalent graphs with 2n nodes.
[ "0", "4", "120", "33600", "18446400", "18361728000", "30199104936000", "76326119565696000", "280889824362219072000", "1443428429045578335360000", "10016498030869925136622080000", "91330153089556497015273454080000" ]
[ "nonn" ]
12
1
2
[ "A002829", "A006607", "A286757" ]
[ "M3711" ]
N. J. A. Sloane.
2017-05-13T23:24:26
oeisdata/seq/A006/A006607.seq
4c2b97dca966af608e0a4d7966638b6a
A006608
Number of n-node graphs not determined by their spectrum.
[ "0", "0", "0", "0", "2", "10", "110", "1722", "51039", "2560606", "215331676", "31067572481" ]
[ "nonn", "hard", "more" ]
36
1
5
[ "A006608", "A099881", "A099882", "A178925" ]
[ "M1981" ]
N. J. A. Sloane
2024-04-12T11:53:37
oeisdata/seq/A006/A006608.seq
f539d89f24438b85370bfba24db017e2
A006609
Number of cyclic neofields of order n.
[ "1", "2", "3", "8", "19", "64", "225", "928", "3441", "17536", "79259", "454016", "2424195", "15628288", "94471089", "679156224", "4613520889", "36563599360" ]
[ "hard", "nonn", "nice" ]
18
4
2
null
[ "M0882" ]
N. J. A. Sloane, Simon Plouffe
2012-12-13T22:59:50
oeisdata/seq/A006/A006609.seq
8016a7a34ec83e8a0939e88ccae163ba
A006610
Number of n-node trees not determined by their spectra.
[ "0", "0", "0", "0", "0", "0", "0", "2", "10", "8", "60", "119", "415", "826", "2470", "5246", "14944", "32347", "84118" ]
[ "nonn", "more" ]
22
1
8
null
[ "M1959" ]
N. J. A. Sloane.
2022-03-31T21:59:18
oeisdata/seq/A006/A006610.seq
34e2ee04ede4068bded5e43f9ef32cd5
A006611
Number of n-node forests not determined by their spectra.
[ "0", "0", "0", "0", "0", "2", "4", "14", "38", "89", "234", "581", "1471", "3560", "8940", "21229", "52876", "126393", "309993" ]
[ "nonn" ]
17
1
6
[ "A005195", "A006611" ]
[ "M1273" ]
N. J. A. Sloane.
2022-03-31T22:00:03
oeisdata/seq/A006/A006611.seq
dddb748543d1ec714319ddba4b7dd3d2
A006612
Number of n-node bipartite graphs not determined by their spectra.
[ "0", "0", "0", "0", "2", "6", "21", "75", "411", "2114", "13529", "108243" ]
[ "nonn" ]
13
1
5
null
[ "M1654" ]
N. J. A. Sloane.
2017-05-15T18:19:33
oeisdata/seq/A006/A006612.seq
eaf9487b52b0c55d71d5f2610a573141
A006613
Zarankiewicz's problem.
[ "8", "13", "17", "22", "29", "34", "40", "47", "56" ]
[ "nonn", "more" ]
15
3
1
null
[ "M4484" ]
N. J. A. Sloane
2021-12-26T21:51:21
oeisdata/seq/A006/A006613.seq
3a735959aac41594a8e6d8a1127f8281
A006614
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all-ones 2 X 4 submatrix.
[ "14", "21", "26", "32", "41", "48", "56", "67" ]
[ "nonn", "more" ]
28
4
1
[ "A001197", "A001198", "A006613", "A006614", "A006615", "A006616", "A006617", "A006618", "A006619", "A006620", "A006621", "A006622", "A006623", "A006624", "A006625", "A006626", "A072567", "A191873", "A191965", "A205805", "A347473", "A347474", "A350237", "A350304" ]
[ "M4925" ]
N. J. A. Sloane
2024-11-05T12:13:15
oeisdata/seq/A006/A006614.seq
c088d8efd4bbeaeab64866657c8c0a9f
A006615
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.
[ "15", "22", "31", "38", "46", "57" ]
[ "nonn", "more" ]
24
4
1
[ "A001197", "A001198", "A006613", "A006614", "A006615", "A006616", "A006617", "A006618", "A006619", "A006620", "A006621", "A006622", "A006623", "A006624", "A006625", "A006626", "A072567", "A191873", "A191965", "A205805", "A347473", "A347474", "A350237", "A350304" ]
[ "M4960" ]
N. J. A. Sloane
2024-03-22T18:04:00
oeisdata/seq/A006/A006615.seq
ed2489071ddd229a13131f8dd9d12f8c
A006616
Zarankiewicz's problem k_4(n).
[ "16", "23", "32", "43", "52", "62", "75", "87", "101", "118" ]
[ "nonn", "hard", "more" ]
23
4
1
[ "A001197", "A001198", "A006616", "A006626", "A339635", "A347474" ]
[ "M4998" ]
N. J. A. Sloane
2024-11-05T12:13:25
oeisdata/seq/A006/A006616.seq
5463153417f5d2f55bbe1978dd6d08d6
A006617
Zarankiewicz's problem.
[ "6", "10", "14", "19", "25", "30", "36", "43", "51", "57" ]
[ "nonn", "more" ]
17
2
1
null
[ "M4083" ]
N. J. A. Sloane
2021-12-26T21:51:58
oeisdata/seq/A006/A006617.seq
abd5bbb28b9b2ff2edf26807cc8b0706
A006618
Zarankiewicz's problem.
[ "11", "17", "22", "28", "36", "43", "51", "61" ]
[ "nonn", "more" ]
17
3
1
null
[ "M4775" ]
N. J. A. Sloane
2021-12-26T21:51:34
oeisdata/seq/A006/A006618.seq
ac1f169d5d4d0f78a7f3eb0020b195be
A006619
Zarankiewicz's problem.
[ "8", "13", "18", "24", "31", "38", "46", "55" ]
[ "nonn", "more" ]
16
2
1
null
[ "M4485" ]
N. J. A. Sloane
2021-12-26T21:51:42
oeisdata/seq/A006/A006619.seq
d68cd384a56d8cecdb99f4c95622c633
A006620
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 2 X 2 submatrix.
[ "5", "8", "11", "15", "19", "23", "27", "32", "37", "43", "49", "54", "59", "64" ]
[ "nonn", "more" ]
23
2
1
[ "A001197", "A001198", "A006613", "A006614", "A006615", "A006616", "A006617", "A006618", "A006619", "A006620", "A006621", "A006622", "A006623", "A006624", "A006625", "A006626", "A072567", "A191873", "A191965", "A205805", "A347473", "A347474", "A350237", "A350304" ]
[ "M3775" ]
N. J. A. Sloane
2024-03-22T18:02:30
oeisdata/seq/A006/A006620.seq
07e24813826531e2128015a61f250899
A006621
Zarankiewicz's problem k_3(n,n+1).
[ "11", "17", "23", "30", "38", "46", "55", "65", "75", "87" ]
[ "nonn", "more" ]
20
3
1
[ "A001198", "A006620", "A006621", "A006626" ]
[ "M4776" ]
N. J. A. Sloane
2021-12-26T18:26:33
oeisdata/seq/A006/A006621.seq
da47479634ef51a4d2b067dac33a691b
A006622
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.
[ "12", "18", "26", "33", "41", "51" ]
[ "nonn", "more" ]
22
3
1
[ "A001197", "A001198", "A006613", "A006614", "A006615", "A006616", "A006617", "A006618", "A006619", "A006620", "A006621", "A006622", "A006623", "A006624", "A006625", "A006626", "A072567", "A191873", "A191965", "A205805", "A347473", "A347474", "A350237", "A350304" ]
[ "M4826" ]
N. J. A. Sloane
2024-03-22T18:04:30
oeisdata/seq/A006/A006622.seq
f32040afb0093b35462e4cbf08b8b801
A006623
Zarankiewicz's problem.
[ "10", "15", "20", "25", "32", "37", "43", "51" ]
[ "nonn", "more" ]
15
4
1
null
[ "M4681" ]
N. J. A. Sloane.
2017-05-18T09:58:16
oeisdata/seq/A006/A006623.seq
70a246464fd8aaa72f29a3393e63f618
A006624
a(n) is the least k such that every n X (n+3) {0,1}-matrix with k ones contains an all-ones 2 X 4 submatrix.
[ "9", "14", "20", "27", "33", "41", "49", "57" ]
[ "nonn", "more" ]
24
2
1
null
[ "M4600" ]
N. J. A. Sloane
2024-02-04T18:43:31
oeisdata/seq/A006/A006624.seq
5272621192ad7f830ccdd7b2307c41ef
A006625
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+2) {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.
[ "14", "21", "28", "36", "45", "55" ]
[ "nonn", "more" ]
22
3
1
[ "A001197", "A001198", "A006613", "A006614", "A006615", "A006616", "A006617", "A006618", "A006619", "A006620", "A006621", "A006622", "A006623", "A006624", "A006625", "A006626", "A072567", "A191873", "A191965", "A205805", "A347473", "A347474", "A350237", "A350304" ]
[ "M4926" ]
N. J. A. Sloane
2024-03-22T18:05:01
oeisdata/seq/A006/A006625.seq
4221685393f7cf0e898d98dc249dec60
A006626
Zarankiewicz's problem k_4(n,n+1).
[ "19", "27", "37", "46", "56", "68", "80", "94", "109" ]
[ "nonn", "more" ]
18
4
1
[ "A006616", "A006620", "A006621", "A006626" ]
[ "M5071" ]
N. J. A. Sloane
2021-12-26T18:26:15
oeisdata/seq/A006/A006626.seq
e773709743bf34e13d2df773805b5220
A006627
Number of nonisomorphic 2-graphs with n nodes with first and second cohomology invariants both 0.
[ "1", "1", "2", "3", "7", "14", "54", "224", "2038", "32728" ]
[ "nonn", "nice" ]
18
1
3
[ "A002854", "A006627", "A085617" ]
[ "M0842" ]
N. J. A. Sloane
2021-12-19T00:04:25
oeisdata/seq/A006/A006627.seq
9e308607bdb13c22eed50fc525472b1f
A006628
From a partition of the integers.
[ "1", "3", "7", "17", "31", "42", "54", "122", "143", "167", "211", "258", "414", "469", "525", "582", "640", "699", "759", "820", "882", "945", "1009", "1075", "1458", "1539", "1621" ]
[ "nonn" ]
11
1
2
null
[ "M2661" ]
N. J. A. Sloane.
2017-05-22T19:19:33
oeisdata/seq/A006/A006628.seq
f51b2aa6d3871b53b23bb26719feafdf
A006629
Self-convolution 4th power of A001764, which enumerates ternary trees.
[ "1", "4", "18", "88", "455", "2448", "13566", "76912", "444015", "2601300", "15426840", "92431584", "558685348", "3402497504", "20858916870", "128618832864", "797168807855", "4963511449260", "31032552351570", "194743066471800", "1226232861415695" ]
[ "nonn", "easy" ]
55
0
2
[ "A000139", "A001764", "A006013", "A006629", "A006630", "A006631", "A092276", "A230547", "A233657" ]
[ "M3542" ]
Simon Plouffe, N. J. A. Sloane
2024-11-29T23:50:24
oeisdata/seq/A006/A006629.seq
2966b7bae2e81f1d4b6b4c6d8391cefe
A006630
From generalized Catalan numbers.
[ "1", "6", "33", "182", "1020", "5814", "33649", "197340", "1170585", "7012200", "42364476", "257854776", "1579730984", "9734161206", "60290077905", "375138262520", "2343880406595", "14699630061270", "92502956574105", "583920410197950", "3696470074992240", "23461536762704040", "149270218961671548" ]
[ "nonn", "easy" ]
63
0
2
[ "A000139", "A006630", "A092276" ]
[ "M4214" ]
Simon Plouffe
2024-02-23T10:16:12
oeisdata/seq/A006/A006630.seq
10786c55c45e6c1f14f4e2ad703fd932
A006631
From generalized Catalan numbers.
[ "1", "8", "52", "320", "1938", "11704", "70840", "430560", "2629575", "16138848", "99522896", "616480384", "3834669566", "23944995480", "150055305008", "943448717120", "5949850262895", "37628321318280", "238591135349700", "1516500543586560", "9660632784642840", "61670325204822048", "394451619337629792" ]
[ "nonn", "easy" ]
27
0
2
[ "A006631", "A092276" ]
[ "M4539" ]
Simon Plouffe
2018-02-25T22:51:42
oeisdata/seq/A006/A006631.seq
76736c83d2dc86b036680888b4acf1cd
A006632
a(n) = 3*binomial(4*n-1,n-1)/(4*n-1).
[ "1", "3", "15", "91", "612", "4389", "32890", "254475", "2017356", "16301164", "133767543", "1111731933", "9338434700", "79155435870", "676196049060", "5815796869995", "50318860986108", "437662920058980", "3824609516638444", "33563127932394060", "295655735395397520", "2613391671568320765" ]
[ "nonn", "easy" ]
104
1
2
[ "A000108", "A000260", "A002293", "A006013", "A006632", "A069271", "A112385", "A120588", "A130564" ]
[ "M2997" ]
Simon Plouffe
2024-12-14T10:26:24
oeisdata/seq/A006/A006632.seq
c031f4eeb4eb194be88eed55b4f3b018
A006633
Expansion of hypergeom([3/2, 7/4, 2, 9/4], [7/3, 8/3, 3], (256/27)*x).
[ "1", "6", "39", "272", "1995", "15180", "118755", "949344", "7721604", "63698830", "531697881", "4482448656", "38111876530", "326439471960", "2814095259675", "24397023508416", "212579132600076", "1860620845932216", "16351267454243260", "144222309948974400", "1276307560533365955", "11329053395044653180" ]
[ "nonn" ]
40
0
2
[ "A000027", "A000260", "A006631", "A006632", "A006633", "A006634", "A006635" ]
[ "M4230" ]
Simon Plouffe
2024-02-25T09:08:59
oeisdata/seq/A006/A006633.seq
9fa392d9276fdb3533132cb05bf86c1a
A006634
From generalized Catalan numbers.
[ "1", "9", "72", "570", "4554", "36855", "302064", "2504304", "20974005", "177232627", "1509395976", "12943656180", "111676661460", "968786892675", "8445123522144", "73940567860896", "649942898236596", "5733561315124260", "50744886833898400", "450461491952952690", "4009721145437152530", "35782256673785401065" ]
[ "nonn" ]
37
0
2
null
[ "M4648" ]
Simon Plouffe
2019-12-15T08:37:38
oeisdata/seq/A006/A006634.seq
7fb7a1d94dc35741296dfaedd93683fd
A006635
From generalized Catalan numbers.
[ "1", "12", "114", "1012", "8775", "75516", "649264", "5593068", "48336171", "419276660", "3650774820", "31907617560", "279871768995", "2463161027292", "21747225841440", "192575673551584", "1710009515037060", "15223466050169520", "135853465827080970", "1215067013768834100" ]
[ "nonn" ]
33
0
2
[ "A002293", "A006633", "A006634", "A006635", "A196678", "A233658", "A233666", "A233667" ]
[ "M4860" ]
Simon Plouffe
2024-11-29T23:50:45
oeisdata/seq/A006/A006635.seq
20c00b7b080d5f4ec3d6b7c21612dbb8
A006636
From generalized Catalan numbers.
[ "8", "36", "102", "231", "456", "819", "1372", "2178", "3312", "4862", "6930", "9633", "13104", "17493", "22968", "29716", "37944", "47880", "59774", "73899", "90552", "110055", "132756", "159030", "189280", "223938", "263466", "308357", "359136", "416361", "480624", "552552", "632808", "722092", "821142", "930735" ]
[ "nonn", "easy" ]
28
0
1
[ "A006636", "A181289" ]
[ "M4516" ]
Simon Plouffe
2023-03-21T17:39:17
oeisdata/seq/A006/A006636.seq
de01466fc7c6553d2582b0fcda7e7390
A006637
From generalized Catalan numbers.
[ "16", "96", "344", "952", "2241", "4712", "9108", "16488", "28314", "46552", "73788", "113360", "169507", "247536", "354008", "496944", "686052", "932976", "1251568", "1658184", "2172005", "2815384", "3614220", "4598360", "5802030", "7264296", "9029556", "11148064", "13676487", "16678496" ]
[ "nonn", "easy" ]
15
0
1
[ "A006637", "A181289" ]
[ "M5005" ]
Simon Plouffe
2022-06-18T19:14:35
oeisdata/seq/A006/A006637.seq
8dc59ba0f63ada9e9ac28913e6069c60
A006638
Restricted postage stamp problem with n denominations and 2 stamps.
[ "2", "4", "8", "12", "16", "20", "26", "32", "40", "44", "54", "64", "72", "80", "92", "104", "116", "128", "140", "152", "164", "180", "196", "212", "228", "244", "262", "280", "298", "316", "338", "360", "382", "404", "426", "448", "470", "492", "514", "536", "562", "588", "614", "644", "674", "704", "734" ]
[ "nonn" ]
30
1
1
[ "A001212", "A006638" ]
[ "M1088" ]
N. J. A. Sloane.
2015-03-14T19:28:52
oeisdata/seq/A006/A006638.seq
e153574c36d447ebb2f0dd1f3c0c8379
A006639
Restricted postage stamp problem.
[ "3", "6", "15", "24", "33", "48", "63", "90" ]
[ "nonn" ]
7
1
1
null
[ "M2581" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006639.seq
31d79690fbf52f082f4fade03ab21831
A006640
Restricted postage stamp problem.
[ "4", "8", "24", "40", "60", "88" ]
[ "nonn" ]
7
1
1
null
[ "M3342" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006640.seq
26528ec1db31f54aeb194c8ac767872e
A006641
Class number of forms with discriminant -A003657(n), or equivalently class number of imaginary quadratic field with discriminant -A003657(n).
[ "1", "1", "1", "1", "1", "2", "1", "2", "3", "2", "3", "2", "4", "2", "1", "5", "2", "2", "4", "4", "3", "1", "4", "7", "5", "3", "4", "6", "2", "2", "8", "5", "6", "3", "8", "2", "6", "10", "4", "2", "5", "5", "4", "4", "3", "10", "2", "7", "6", "4", "10", "1", "8", "11", "4", "5", "8", "4", "2", "13", "4", "9", "4", "3", "6", "14", "4", "7", "5", "4", "12", "2" ]
[ "nonn", "easy", "nice" ]
37
1
6
[ "A003657", "A006641" ]
[ "M0112" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006641.seq
8bb5d67fc09c8cf7b8d94c99de956bc0
A006642
Class number of quadratic field with discriminant -4n+1.
[ "1", "1", "1", "2", "1", "3", "3", "2", "4", "1", "5", "2", "4", "3", "1", "7", "5", "3", "6", "2", "8", "5", "3", "8", "2", "10", "2", "5", "5", "3", "10", "7", "4", "10", "1", "11", "5", "8", "2", "13", "4", "9", "4", "3", "14", "4", "7", "5", "12", "2", "15", "6", "7", "12", "4", "13", "2", "11", "3", "14", "4", "8", "8", "10", "3", "19", "10", "4" ]
[ "nonn" ]
11
1
4
[ "A006642", "A006643" ]
[ "M0152" ]
N. J. A. Sloane, Mira Bernstein
2014-01-27T08:54:41
oeisdata/seq/A006/A006642.seq
ab5e1807cc2eba0d25cdd597a08a73c4
A006643
Class number of quadratic field with discriminant -4n as n runs through A089269: squarefree numbers congruent to 1 or 2 mod 4.
[ "1", "1", "2", "2", "2", "2", "4", "4", "4", "2", "6", "6", "4", "4", "4", "2", "6", "8", "4", "4", "6", "4", "2", "6", "8", "8", "8", "8", "4", "4", "10", "8", "4", "4", "4", "10", "12", "4", "8", "4", "14", "4", "8", "6", "6", "12", "8", "8", "6", "10", "12", "4", "4", "14", "8", "8", "8", "4", "8", "16", "14", "8", "6", "8", "16", "8", "10", "12", "14", "12", "4", "8", "10", "12", "16", "12", "4", "4", "20", "10", "12", "6", "8", "20", "20", "8", "8", "6", "8", "10", "16" ]
[ "nonn" ]
24
1
3
[ "A000003", "A006642", "A006643", "A014599", "A089269" ]
[ "M0225" ]
N. J. A. Sloane, Mira Bernstein
2018-01-27T06:30:56
oeisdata/seq/A006/A006643.seq
afad7a7814bab2becb9cc48dbe444333
A006644
Indices of records in Landau's function A000793.
[ "0", "2", "3", "4", "5", "7", "8", "9", "10", "12", "14", "15", "16", "17", "19", "23", "25", "27", "28", "29", "30", "32", "34", "36", "38", "40", "41", "42", "43", "47", "49", "53", "57", "58", "59", "60", "62", "64", "66", "68", "70", "72", "76", "77", "78", "79", "83", "85", "89", "93", "95", "97", "101", "102", "106", "108", "112", "118", "120", "126", "128", "130", "131", "132" ]
[ "nonn" ]
18
1
2
[ "A000793", "A002809", "A006644" ]
null
N. J. A. Sloane.
2019-08-24T09:38:31
oeisdata/seq/A006/A006644.seq
91e681aae4e0e64d104b291bf71d8f45
A006645
Self-convolution of Pell numbers (A000129).
[ "0", "0", "1", "4", "14", "44", "131", "376", "1052", "2888", "7813", "20892", "55338", "145428", "379655", "985520", "2545720", "6547792", "16777993", "42847988", "109099078", "277040572", "701794187", "1773851304", "4474555476", "11266301976", "28318897549", "71070913036", "178106093666", "445740656420", "1114147888655" ]
[ "nonn", "easy" ]
58
0
4
[ "A006645", "A054456", "A054457" ]
null
N. J. A. Sloane
2024-03-01T09:59:32
oeisdata/seq/A006/A006645.seq
8dce23397d814a676d4d46622c6151a8
A006646
Exponential self-convolution of Pell numbers.
[ "0", "0", "2", "12", "64", "320", "1568", "7616", "36864", "178176", "860672", "4156416", "20070400", "96911360", "467935232", "2259402752", "10909384704", "52675215360", "254338531328", "1228055248896", "5929575645184", "28630524624896" ]
[ "nonn", "easy" ]
21
0
3
[ "A000129", "A002203", "A006646", "A006668" ]
null
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006646.seq
763c0d2c5a563fb5831208ed442e8c56
A006647
Number of graphs with n nodes, n-2 edges and no isolated vertices.
[ "1", "1", "3", "6", "15", "33", "83", "202", "527", "1377", "3744", "10335", "29297", "84396", "248034", "740289", "2245094", "6904206", "21522973", "67936799", "217026480", "701159919", "2289925258", "7556363054", "25184139149", "84743377436", "287815771822", "986345040471", "3409869008578" ]
[ "nonn" ]
16
4
3
[ "A001430", "A001433", "A006647" ]
[ "M2586" ]
N. J. A. Sloane.
2017-06-05T03:51:44
oeisdata/seq/A006/A006647.seq
e35787b943ce4adbd8b39819315d4045
A006648
Number of graphs with n nodes, n-1 edges and no isolated vertices.
[ "1", "1", "2", "4", "9", "20", "50", "124", "332", "895", "2513", "7172", "20994", "62366", "188696", "578717", "1799999", "5666257", "18047319", "58097540", "188953756", "620493315", "2056582095", "6877206111", "23195975865", "78891742748", "270505303760", "934890953041", "3256230606767" ]
[ "nonn" ]
15
2
3
[ "A001433", "A001434", "A006648" ]
[ "M1181" ]
N. J. A. Sloane.
2017-06-06T04:21:21
oeisdata/seq/A006/A006648.seq
5e924f3ca400684d25169c4ab7dac39e
A006649
Number of graphs with n nodes, n edges and no isolated vertices.
[ "1", "0", "0", "1", "2", "5", "15", "41", "124", "369", "1132", "3491", "10984", "34768", "111514", "360560", "1176797", "3870389", "12829765", "42829894", "143980892", "487227611", "1659499566", "5688046485", "19617965938", "68078878268", "237694501644", "834946053269", "2950683815028", "10490767818951", "37524169403930" ]
[ "nonn" ]
16
0
5
[ "A001434", "A006649", "A008406", "A048179", "A368599" ]
[ "M1474" ]
N. J. A. Sloane
2024-01-09T16:24:08
oeisdata/seq/A006/A006649.seq
7bd53dc0b254a98b6db3433f6bf19cb4
A006650
Number of graphs with n nodes, n+1 edges and no isolated vertices.
[ "1", "5", "20", "73", "271", "974", "3507", "12487", "44475", "157814", "559952", "1985053", "7040855", "24986930", "88782435", "315911844", "1126178655", "4023135764", "14406870196", "51728509807", "186275015554", "672886200335" ]
[ "nonn" ]
10
4
2
[ "A006650", "A048179", "A048180" ]
[ "M3903" ]
N. J. A. Sloane.
2013-05-10T12:43:49
oeisdata/seq/A006/A006650.seq
6f3cecffff1ab3d6f12f2c599babfdfd
A006651
Number of graphs with n nodes, n+2 edges and no isolated vertices.
[ "1", "4", "22", "110", "515", "2272", "9777", "40752", "166519", "668134", "2644988", "10351321", "40150556", "154591610", "591780559", "2254880616", "8561287942", "32418230925", "122522492807", "462502319244", "1744810912396", "6581954720648", "24839735669771" ]
[ "nonn" ]
11
4
2
[ "A006651", "A048180" ]
[ "M3584" ]
N. J. A. Sloane.
2013-05-10T12:43:49
oeisdata/seq/A006/A006651.seq
afcba34cb4c3c92ec526fb5a2d2e065f
A006652
From the graph reconstruction problem.
[ "1", "2", "5", "11", "27", "62", "152", "373" ]
[ "nonn" ]
7
4
2
null
[ "M1401" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006652.seq
bca9bc5f2046138346d04c3dc4bc3ea6
A006653
From the graph reconstruction problem.
[ "1", "2", "6", "14", "36", "89", "229", "599", "1609" ]
[ "nonn" ]
8
3
2
null
[ "M1602" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006653.seq
4809e17740047ea8a2e3be8e715a1d3a
A006654
From the graph reconstruction problem.
[ "2", "6", "14", "38", "97", "264", "728", "2084", "6100" ]
[ "nonn" ]
8
3
1
null
[ "M1605" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006654.seq
a901a6f95e047c9f4488e4385049d756
A006655
From the graph reconstruction problem.
[ "11", "32", "87", "247", "716", "2155", "6694", "21461" ]
[ "nonn" ]
6
4
1
null
[ "M4787" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006655.seq
07ef463eb154253917839dd19606b5c7
A006656
Denominators of expansion of sinh x / sin x.
[ "1", "3", "3", "21", "9", "11", "21", "9", "1", "133", "693", "69", "7", "189", "3", "7161", "231", "7", "399", "63", "77", "3311", "4347", "987", "49", "33", "33", "627", "57", "59", "7161", "2079", "11", "10787", "207", "2343", "1463", "4389", "231", "1659", "6237", "913", "9933", "693", "161", "7301833", "19184319", "4389", "11", "99", "33" ]
[ "nonn", "easy", "frac" ]
27
0
2
[ "A000965", "A006656", "A296628" ]
[ "M2294" ]
N. J. A. Sloane, Simon Plouffe
2022-02-03T06:01:14
oeisdata/seq/A006/A006656.seq
27d9aa131f5d66e6b045d9da35b216f7
A006657
Number of closed meanders with 2 components and 2n bridges.
[ "2", "12", "84", "640", "5236", "45164", "406012", "3772008", "35994184", "351173328", "3490681428", "35253449296", "360946635312", "3739935635756", "39159200588780", "413836299216608", "4409705753032648", "47337525317450816", "511563350415103008" ]
[ "nonn", "nice" ]
32
2
1
[ "A005315", "A006657", "A008828" ]
[ "M2037" ]
N. J. A. Sloane, Simon Plouffe
2022-06-17T12:24:48
oeisdata/seq/A006/A006657.seq
fa3316f7cb35b90d5806b52c160c0ad2
A006658
Closed meanders with 3 components and 2n bridges.
[ "5", "56", "580", "5894", "60312", "624240", "6540510", "69323910", "742518832", "8028001566", "87526544560", "961412790002", "10630964761766", "118257400015312", "1322564193698320", "14863191405246888", "167771227744292160", "1901345329566422790" ]
[ "nonn" ]
29
3
1
[ "A005315", "A006657", "A006658", "A008828" ]
[ "M4014" ]
N. J. A. Sloane
2019-09-25T07:46:15
oeisdata/seq/A006/A006658.seq
c4064fd94667d976052f7c1525b82416
A006659
Number of closed meander systems of order n+1 with n components.
[ "2", "12", "56", "240", "990", "4004", "16016", "63648", "251940", "994840", "3922512", "15452320", "60843510", "239519700", "942871200", "3711935040", "14615744220", "57562286760", "226760523600", "893550621600", "3522078700140", "13887053160552" ]
[ "nonn", "easy", "nice" ]
78
1
1
[ "A001622", "A002057", "A002694", "A005315", "A005316", "A006659", "A008828" ]
[ "M2025" ]
D. Ivanov, S. K. Lando and A. K. Zvonkin (zvonkin(AT)labri.u-bordeaux.fr)
2022-06-17T03:23:28
oeisdata/seq/A006/A006659.seq
588808725282b07bc0a63828e7a216a8
A006660
Number of meanders in which first bridge is 3.
[ "1", "1", "2", "3", "7", "14", "36", "81", "221", "538", "1530", "3926", "11510", "30694", "92114", "252939", "773259", "2172830", "6743122", "19304190", "60658606", "176343390", "559952824", "1649008456", "5283239596", "15730575554", "50789908772", "152663683494" ]
[ "nonn" ]
26
3
3
[ "A005316", "A006660", "A259974" ]
[ "M0840" ]
Simon Plouffe
2017-06-28T15:17:07
oeisdata/seq/A006/A006660.seq
266d213f3ff5ccd8b768057fa3954294
A006661
Number of meanders in which first bridge is 5.
[ "3", "3", "7", "11", "28", "57", "155", "353", "1003", "2458", "7214", "18575", "55880", "149183", "457639", "1255933", "3914103", "10978240", "34663182", "98953078", "315884786", "915008430", "2948378068", "8645874055", "28084475514", "83222134020" ]
[ "nonn" ]
28
5
1
[ "A005316", "A006661", "A259974" ]
[ "M2286" ]
Simon Plouffe
2017-06-28T15:17:12
oeisdata/seq/A006/A006661.seq
8cfea471739dda7e54c3ab21e3ee94a7
A006662
Number of meanders in which first bridge is 7.
[ "14", "14", "36", "57", "155", "316", "902", "2053", "6059", "14810", "44842", "115009", "355293", "943860", "2963536", "8086913", "25733325", "71725012", "230811370", "654472364", "2126296860", "6115504594", "20032488714", "58309793101" ]
[ "nonn" ]
27
7
1
[ "A005316", "A006662", "A259974" ]
[ "M4921" ]
Simon Plouffe
2017-06-28T15:17:16
oeisdata/seq/A006/A006662.seq
4ad49882422ee0afe1518ac7e759a4c2
A006663
Number of projective meanders.
[ "1", "1", "2", "2", "8", "12", "52", "86", "400", "710", "3404", "6316", "30888", "59204", "293192", "576018", "2877184", "5764430", "28967428", "58970568", "297634344", "614037754", "3109111064" ]
[ "nonn", "nice", "more" ]
30
0
3
null
[ "M0374" ]
N. J. A. Sloane, Simon Plouffe
2017-06-28T15:17:37
oeisdata/seq/A006/A006663.seq
a5c2b4542920ebf0fe01453518aad7b7
A006664
Number of irreducible systems of meanders.
[ "1", "1", "2", "8", "46", "322", "2546", "21870", "199494", "1904624", "18846714", "191955370", "2002141126", "21303422480", "230553207346", "2531848587534", "28159614749270", "316713536035464", "3597509926531778", "41225699113145888", "476180721050626814", "5539597373695447322", "64863295574835126394", "763984568163192551672", "9047263176444565467566" ]
[ "nonn", "nice" ]
37
0
3
null
[ "M1871" ]
N. J. A. Sloane, Simon Plouffe
2023-09-03T21:03:00
oeisdata/seq/A006/A006664.seq
593fbddbfe905d146882ef1490631f25
A006665
G.f.: { ( Product_{j=1..infinity} (1-x^j) - 1 )/x }^24.
[ "1", "24", "276", "2024", "10602", "41952", "128500", "303048", "517155", "463496", "-609684", "-3757992", "-9340852", "-14912280", "-12957624", "8669712", "59707149", "132295080", "183499244", "131501856", "-113698752", "-575221744", "-1111921752", "-1363192680", "-824406065", "889513752", "3638565960", "6404250248" ]
[ "sign" ]
14
0
2
null
[ "M5156" ]
N. J. A. Sloane.
2020-08-24T11:33:50
oeisdata/seq/A006/A006665.seq
ca4ce8b157aae91c06203cd5a0b8426b
A006666
Number of halving steps to reach 1 in '3x+1' problem, or -1 if this never happens.
[ "0", "1", "5", "2", "4", "6", "11", "3", "13", "5", "10", "7", "7", "12", "12", "4", "9", "14", "14", "6", "6", "11", "11", "8", "16", "8", "70", "13", "13", "13", "67", "5", "18", "10", "10", "15", "15", "15", "23", "7", "69", "7", "20", "12", "12", "12", "66", "9", "17", "17", "17", "9", "9", "71", "71", "14", "22", "14", "22", "14", "14", "68", "68", "6", "19", "19", "19", "11", "11", "11", "65", "16", "73", "16", "11", "16" ]
[ "nonn", "nice", "look", "easy" ]
141
1
3
[ "A006370", "A006577", "A006666", "A006667", "A014682", "A092892", "A127789" ]
[ "M3733" ]
N. J. A. Sloane, Bill Gosper
2025-02-16T08:32:30
oeisdata/seq/A006/A006666.seq
d1b844f2d5b1fa55d387f727c1519a8a
A006667
Number of tripling steps to reach 1 from n in '3x+1' problem, or -1 if 1 is never reached.
[ "0", "0", "2", "0", "1", "2", "5", "0", "6", "1", "4", "2", "2", "5", "5", "0", "3", "6", "6", "1", "1", "4", "4", "2", "7", "2", "41", "5", "5", "5", "39", "0", "8", "3", "3", "6", "6", "6", "11", "1", "40", "1", "9", "4", "4", "4", "38", "2", "7", "7", "7", "2", "2", "41", "41", "5", "10", "5", "10", "5", "5", "39", "39", "0", "8", "8", "8", "3", "3", "3", "37", "6", "42", "6", "3", "6", "6", "11", "11", "1", "6", "40", "40", "1", "1", "9", "9", "4", "9", "4", "33", "4", "4", "38" ]
[ "nonn", "nice", "hear" ]
108
1
3
[ "A000079", "A000265", "A006370", "A006577", "A006666", "A006667", "A078719", "A092893", "A127789", "A139391", "A209229" ]
[ "M0019" ]
N. J. A. Sloane and Bill Gosper
2025-04-10T00:11:56
oeisdata/seq/A006/A006667.seq
9d51ab102d36cd67020898fc0711e3e4
A006668
Exponential self-convolution of Pell numbers (divided by 2).
[ "0", "0", "1", "6", "32", "160", "784", "3808", "18432", "89088", "430336", "2078208", "10035200", "48455680", "233967616", "1129701376", "5454692352", "26337607680", "127169265664", "614027624448", "2964787822592", "14315262312448", "69120201588736" ]
[ "nonn", "easy" ]
22
0
4
[ "A002203", "A006646", "A006668" ]
null
N. J. A. Sloane.
2022-09-08T08:44:35
oeisdata/seq/A006/A006668.seq
e80570ee8d6f42c41ed3333298149e8a
A006669
Exponentiation of g.f. for Pell numbers.
[ "0", "1", "2", "8", "32", "159", "882", "5475", "37256", "276004", "2207944", "18949677", "173475876", "1685805913", "17319275430", "187443865596", "2130493441472", "25360318907075", "315370749394134", "4088067189914051", "55128639891893220", "771992274220462744", "11207495397779852000" ]
[ "nonn" ]
10
0
3
[ "A000129", "A006669" ]
null
N. J. A. Sloane.
2017-06-15T02:17:08
oeisdata/seq/A006/A006669.seq
085068e9cb17ebccbd4210f43754becc
A006670
Edge-distinguishing chromatic number of path with n nodes.
[ "1", "1", "2", "2", "3", "3", "3", "4", "4", "4", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "12" ]
[ "nonn" ]
15
1
3
null
[ "M0252" ]
N. J. A. Sloane.
2017-06-14T14:13:52
oeisdata/seq/A006/A006670.seq
abd8e5a135a2b0ad5811004f7a120e2e
A006671
Edge-distinguishing chromatic number of cycle with n nodes.
[ "3", "3", "3", "3", "4", "4", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "13", "13" ]
[ "nonn" ]
20
3
1
null
[ "M2269" ]
N. J. A. Sloane.
2017-06-14T14:14:42
oeisdata/seq/A006/A006671.seq
0eeec8fa6cea6cd70fd2e963abff63c3
A006672
Ramsey numbers.
[ "4", "4", "6", "7", "8", "9", "11", "12", "13", "14" ]
[ "nonn" ]
22
1
1
null
[ "M3226" ]
N. J. A. Sloane
2016-05-03T17:03:14
oeisdata/seq/A006/A006672.seq
abf3cc425e99e17607ddfb4df19a61ac
A006673
E.g.f. is the logarithmic derivative of e.g.f. for Pell numbers [1, 0, 1, 2, 5, ...].
[ "0", "1", "2", "2", "-8", "-56", "-112", "848", "9088", "25216", "-310528", "-4334848", "-14701568", "270029824", "4554426368", "17536821248", "-458243735552", "-8926669144064", "-37024075153408", "1341521605885952", "29290212127670272", "125297096967061504", "-6224109737622372352" ]
[ "sign" ]
58
0
3
[ "A000129", "A006673" ]
null
N. J. A. Sloane
2020-04-22T16:14:29
oeisdata/seq/A006/A006673.seq
e7c2948ee304f3055f0e4aa1df9981a2
A006674
Triangulations of a square with no separating triangles (previously "Bordered triangulations of sphere with n nodes").
[ "1", "1", "2", "6", "18", "68", "282", "1309", "6437", "33264", "177260", "968349" ]
[ "nonn" ]
16
5
3
null
[ "M1631" ]
N. J. A. Sloane
2024-06-01T10:14:53
oeisdata/seq/A006/A006674.seq
1102976cdf41575f13a74604a152ff09
A006675
Number of paths through an array.
[ "0", "0", "2", "15", "104", "770", "6264", "56196", "554112", "5973264", "69998400", "886897440", "12089295360", "176484597120", "2748022986240", "45472329504000", "796983880089600", "14751208762214400", "287543058350284800" ]
[ "nonn", "easy", "nice" ]
23
0
3
[ "A000254", "A001705", "A006675" ]
[ "M2079" ]
N. J. A. Sloane
2021-12-18T22:20:31
oeisdata/seq/A006/A006675.seq
f9cd432df2ab45828376307638a9fd98
A006676
Number of paths through an array.
[ "6", "104", "1345", "16344", "200452", "2552192", "34138908", "482076000", "7196676696", "113548220928", "1891322394624", "33205209053184", "613390541616000", "11900521690398720", "242050276080034560", "5152173699467335680", "114574144611434273280" ]
[ "nonn" ]
14
3
1
null
[ "M4292" ]
N. J. A. Sloane.
2017-06-16T19:28:36
oeisdata/seq/A006/A006676.seq
72147c549d5abf0ea0ac38ce2785cd3d
A006677
Number of planted binary phylogenetic trees with n labels.
[ "1", "2", "7", "41", "346", "3797", "51157", "816356", "15050581", "314726117", "7359554632", "190283748371", "5389914888541", "165983936096162", "5521346346543307", "197294173392918461", "7536892461493548226", "306520422583290179057", "13222422454704116605057", "603006160203712090160876" ]
[ "nonn", "nice", "easy" ]
63
1
2
null
[ "M1806" ]
N. J. A. Sloane, Simon Plouffe
2019-12-14T21:41:42
oeisdata/seq/A006/A006677.seq
e3ac7e6cac04297dabb11dc3d257cdf3
A006678
Number of planted binary phylogenetic trees with n labels.
[ "0", "1", "1", "6", "39", "390", "4815", "73080", "1304415", "26847450", "625528575", "16279193700", "468022452975", "14731683916950", "503880434632575", "18609309606888000", "738057377647965375", "31286068076704691250", "1411602439003747365375", "67543694966494692445500", "3416288904242387117319375" ]
[ "nonn" ]
29
0
4
null
[ "M4232" ]
N. J. A. Sloane, Simon Plouffe
2025-01-08T09:31:04
oeisdata/seq/A006/A006678.seq
e3163a4369eecc632af7159a33480faf
A006679
Number of planted binary phylogenetic trees with n labels.
[ "0", "1", "2", "10", "83", "946", "13772", "244315", "5113208", "123342166", "3369568817", "102831001120", "3467225430308", "128006254663561", "5135734326127862", "222498607683528550", "10352141336173618883", "514815201125079097006", "27251316075035460318032", "1529842445683171428183355" ]
[ "nonn" ]
40
0
3
null
[ "M1978" ]
N. J. A. Sloane, Simon Plouffe
2018-01-10T16:11:11
oeisdata/seq/A006/A006679.seq
cfc8acebcb73af15e20b9ad5ac2904eb
A006680
Number of binary phylogenetic trees with n labels.
[ "1", "1", "7", "45", "465", "5775", "88515", "1588545", "32852925", "768242475", "20053670175", "577971719325", "18230691904425", "624676513836375", "23106221910646875", "917643290676737625", "38944796393877499125", "1759004961887566267875" ]
[ "nonn" ]
16
2
3
null
[ "M4427" ]
N. J. A. Sloane.
2018-01-10T16:11:18
oeisdata/seq/A006/A006680.seq
76d2df2ae59c338dd43845b64ebb15ea
A006681
Number of binary phylogenetic trees with n labels.
[ "1", "4", "16", "85", "646", "6664", "86731", "1354630", "24607816", "509000899", "11802833296", "303129872500", "8539567141561", "261785254856584", "8674697402099836", "308953306192527445", "11768768651529113506", "477433786852228938844" ]
[ "nonn" ]
22
2
2
null
[ "M3527" ]
N. J. A. Sloane.
2024-09-05T08:07:47
oeisdata/seq/A006/A006681.seq
7906f26171503fd165d35958fdbabca3
A006682
Number of binary phylogenetic trees with n labels.
[ "1", "4", "20", "155", "1716", "24654", "434155", "9043990", "217457456", "5926620029", "180538177590", "6078622845750", "224156328707221", "8984765008810504", "388939866084222200", "18083736252080051435", "898779656769444326136", "47551736771345760732954" ]
[ "nonn" ]
16
2
2
null
[ "M3571" ]
N. J. A. Sloane.
2018-01-10T16:11:34
oeisdata/seq/A006/A006682.seq
862ccf7d86b352ccdb094cb0e38aecda
A006683
Number of regions in certain maps.
[ "1", "2", "3", "4", "6", "8", "11", "15", "21", "28", "39", "53", "99", "137", "186" ]
[ "nonn" ]
8
1
2
null
[ "M0560" ]
N. J. A. Sloane.
2012-03-30T16:45:02
oeisdata/seq/A006/A006683.seq
7926eba49b88314c2806e391f8639043
A006684
Convolve Fibonacci and Pell numbers.
[ "0", "0", "1", "3", "9", "24", "62", "156", "387", "951", "2323", "5652", "13716", "33228", "80405", "194415", "469845", "1135092", "2741626", "6620928", "15987663", "38603019", "93204647", "225030024", "543293352", "1311663096", "3166694569", "7645173627", "18457238241", "44559967920", "107577688310", "259716176580" ]
[ "nonn" ]
50
0
4
[ "A000045", "A000129", "A006684", "A106515" ]
null
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006684.seq
9d37adac2cd3a73f9269cc78e8a1455f
A006685
Coefficients for numerical integration.
[ "24", "1920", "193536", "66355200", "13624934400", "243465191424000", "4944216195072000", "9990141980442624000", "39391717484295880704000", "465236915972420822630400000" ]
[ "nonn" ]
20
0
1
[ "A002197", "A002198", "A006685" ]
[ "M5173" ]
N. J. A. Sloane
2017-06-17T09:47:40
oeisdata/seq/A006/A006685.seq
e5ab19cdf5f5b99d773f52c23f959107
A006686
Octavan primes: primes of the form p = x^8 + y^8.
[ "2", "257", "65537", "2070241", "100006561", "435746497", "815730977", "832507937", "1475795617", "2579667841", "4338014017", "5110698017", "6975822977", "16983628577", "17995718017", "25605764801", "32575757441", "37822859617", "37839636577", "54875880097" ]
[ "nonn" ]
35
1
1
[ "A000040", "A003380", "A006686", "A291206" ]
[ "M5428" ]
N. J. A. Sloane
2021-12-26T21:50:25
oeisdata/seq/A006/A006686.seq
e767ace40180cf50ce3690f78ef34f9c
A006687
Duodecimal primes: p = (x^12 + y^12 )/(x^4 + y^4 ).
[ "241", "5521", "6481", "51361", "346561", "380881", "390001", "1678321", "4332721", "4654801", "5576881", "12707521", "39336721", "41432641", "42942001", "99990001", "167948881", "184970641", "197063761", "205598881" ]
[ "nonn" ]
12
1
1
null
[ "M5418" ]
N. J. A. Sloane.
2015-07-25T13:22:28
oeisdata/seq/A006/A006687.seq
e7b92da2416a52326e451a865e12ff41
A006688
Number of self-dual equivalence classes switching functions of exactly n+1 variables.
[ "1", "0", "2", "4", "76", "109875" ]
[ "nonn", "nice" ]
16
0
3
[ "A001531", "A006688" ]
[ "M1305" ]
N. J. A. Sloane
2021-12-18T20:54:21
oeisdata/seq/A006/A006688.seq
1c311959020b463609130dea89f20c57
A006689
Number of deterministic, completely-defined, initially-connected finite automata with 2 inputs and n unlabeled states.
[ "1", "12", "216", "5248", "160675", "5931540", "256182290", "12665445248", "705068085303", "43631250229700", "2970581345516818", "220642839342906336", "17753181687544516980", "1538156947936524172656", "142767837727544113783650" ]
[ "easy", "nonn" ]
69
1
2
[ "A006689", "A006690", "A107667", "A107670" ]
[ "M4876" ]
N. J. A. Sloane
2021-03-11T02:46:07
oeisdata/seq/A006/A006689.seq
2dc27b2d40e7c3be49350715c320b365
A006690
Number of deterministic, completely-defined, initially-connected finite automata with 3 inputs and n unlabeled states.
[ "1", "56", "7965", "2128064", "914929500", "576689214816", "500750172337212", "572879126392178688", "835007874759393878655", "1510492370204314777345000", "3320470273536658970739763334", "8718034433102107344888781813632", "26945647825926481227016730431025962", "96843697086370972449408988324175689680" ]
[ "easy", "nonn" ]
67
1
2
[ "A006689", "A006690", "A107671", "A107676" ]
[ "M5316" ]
N. J. A. Sloane
2021-03-08T22:29:51
oeisdata/seq/A006/A006690.seq
9b1ce4d9376c80e9fbed77c33922e8f8
A006691
Normalized number of connected (n+1)-state finite automata with 2 inputs.
[ "9", "148", "3493", "106431", "3950832", "172325014", "8617033285", "485267003023", "30363691715629", "2088698040637242", "156612539215405732", "12709745319947141220", "1109746209390479579732", "103724343230007402591558" ]
[ "nonn" ]
54
1
1
[ "A006691", "A027834", "A304312" ]
[ "M4662" ]
N. J. A. Sloane.
2021-02-27T11:00:52
oeisdata/seq/A006/A006691.seq
73691b5de83a329d60e7ae76d0e0f7af
A006692
Number of connected n-state finite automata with 3 inputs.
[ "49", "6877", "1854545", "807478656", "514798204147", "451182323794896", "519961864703259753", "762210147961330421167", "1384945048774500147047194", "3055115321627096660341307614", "8043516699726480852467167758419", "24915939138210507189761922944830006" ]
[ "nonn" ]
27
1
1
[ "A006691", "A006692", "A027834", "A304313" ]
[ "M5298" ]
N. J. A. Sloane.
2021-03-11T03:00:24
oeisdata/seq/A006/A006692.seq
108119908a7702732d38d42678802483
A006693
Modified Engel expansion of 3/7.
[ "2", "4", "5", "7", "8", "10", "25", "53", "62", "134", "574", "2431", "13147", "27167", "229073", "315416", "435474", "771789", "1522716", "3853889", "7878986", "7922488", "8844776", "9182596", "9388467", "14781524", "135097360", "1374449987", "1561240840", "4408239956", "11166053604", "12014224315" ]
[ "nonn" ]
27
1
1
null
[ "M0960" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006693.seq
bf58ef676b1abd6cb71a6b0fb281e55b
A006694
Number of cyclotomic cosets of 2 mod 2n+1.
[ "0", "1", "1", "2", "2", "1", "1", "4", "2", "1", "5", "2", "2", "3", "1", "6", "4", "5", "1", "4", "2", "3", "7", "2", "4", "7", "1", "4", "4", "1", "1", "12", "6", "1", "5", "2", "8", "7", "5", "2", "4", "1", "11", "4", "8", "9", "13", "4", "2", "7", "1", "2", "14", "1", "3", "4", "4", "5", "11", "8", "2", "7", "3", "18", "10", "1", "9", "10", "2", "1", "5", "4", "6", "9", "1", "10", "12", "13", "3", "4", "8", "1", "13", "2", "2", "11", "1", "8", "4", "1", "1", "4", "6", "7", "19", "2", "2", "19", "1", "2" ]
[ "nonn", "nice", "easy", "changed" ]
98
0
4
[ "A000010", "A000374", "A001917", "A002326", "A006694", "A037226", "A064286", "A064287", "A081844", "A139767", "A321298", "A357217" ]
[ "M0192" ]
N. J. A. Sloane, Sep 25 2001
2025-04-25T03:06:45
oeisdata/seq/A006/A006694.seq
ecf406ca215640f280971f60add3648b
A006695
a(2n)=2*a(2n-2)^2-1, a(2n+1)=2*a(2n)-1, a(0)=2.
[ "2", "3", "7", "13", "97", "193", "18817", "37633", "708158977", "1416317953", "1002978273411373057", "2005956546822746113", "2011930833870518011412817828051050497", "4023861667741036022825635656102100993" ]
[ "nonn", "easy", "nice" ]
31
0
1
[ "A001075", "A001685", "A002715", "A003686", "A006695", "A064526" ]
[ "M0838" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006695.seq
933f446ba2a2b9917d79c6e45c98bf30
A006696
a(n) = min_{k=1..n} (a(k-1) + 2^k*(n + a(n-k))); a(0) = 0.
[ "0", "2", "8", "22", "50", "110", "226", "464", "938", "1888", "3794", "7598", "15208", "30438", "60890", "121792", "243606", "487238", "974488", "1948998", "3898034", "7796078", "15592168", "31184358", "62368754", "124737534", "249475080", "498950182", "997900402", "1995800846", "3991601704", "7983203430", "15966406898" ]
[ "nonn", "nice", "easy" ]
31
0
2
[ "A000079", "A006696" ]
[ "M1836" ]
Jeffrey Shallit, N. J. A. Sloane
2017-08-11T18:54:00
oeisdata/seq/A006/A006696.seq
206779c012b95043da2a27f367b7ca35
A006697
Number of subwords of length n in infinite word generated by a -> aab, b -> b.
[ "1", "2", "4", "6", "9", "13", "17", "22", "28", "35", "43", "51", "60", "70", "81", "93", "106", "120", "135", "151", "167", "184", "202", "221", "241", "262", "284", "307", "331", "356", "382", "409", "437", "466", "496", "527", "559", "591", "624", "658", "693", "729", "766", "804", "843", "883", "924", "966", "1009", "1053", "1098", "1144", "1191", "1239" ]
[ "nonn", "easy", "nice" ]
42
0
2
[ "A005942", "A005943", "A006697", "A094913", "A134457", "A134466" ]
[ "M1001" ]
N. J. A. Sloane and Jeffrey Shallit
2025-01-01T13:10:36
oeisdata/seq/A006/A006697.seq
8b4b16df94a1d27fc3a104794cbc9484
A006698
T(2,2n), where T(k,m) is the number of sequences a_1,...,a_m of integers 0,1,...,n with n=floor(m/k) such that the 'bumped' sequence b_1,...,b_m has exactly k of each of 0,...,n-1, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.
[ "1", "1", "11", "378", "27213", "3378680", "645216039", "175804806912", "64820487788537", "31093204323279744", "18824085922156535715", "14040767751007803601664", "12652731866917353207799557", "13553071929305974778937888768" ]
[ "nonn", "easy" ]
11
0
3
[ "A006698", "A006699", "A006700" ]
[ "M4813" ]
N. J. A. Sloane.
2022-10-30T18:19:58
oeisdata/seq/A006/A006698.seq
e653fa94ba8451d81f7eb85a8fa17c56
A006699
T(3,3n), where T(k,m) is the number of sequences a_1,...,a_m of integers 0,1,...,n with n=floor(m/k) such that the 'bumped' sequence b_1,...,b_m has exactly k of each of 0,...,n-1, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.
[ "1", "1", "42", "9529", "6421892", "9652612995", "27361464052486", "131032872291901741", "980985180215656298952", "10837828798232467724499511", "168999527708576706854487574250", "3590193461689323277342585899536097" ]
[ "nonn", "easy" ]
11
0
3
[ "A006698", "A006699", "A006700" ]
[ "M5282" ]
N. J. A. Sloane.
2022-10-30T18:19:58
oeisdata/seq/A006/A006699.seq
8f09c251548577c2f2e174fbce29a2ef
A006700
T(n,3,1), where T(n,k,s) with 0<=s<n is the number of sequences a_1,...,a_(k*n+s) of integers 0,1,...,n such that the 'bumped' sequence b_1,...,b_(k*n+s) has exactly s n's, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.
[ "1", "5", "393", "131473", "117316993", "219639324573", "745567087151089", "4160071323762705545", "35561839228620292884321", "441709871992325805279854773", "7649447738065395278958097645657" ]
[ "nonn", "easy" ]
11
0
2
[ "A006698", "A006699", "A006700" ]
[ "M4038" ]
N. J. A. Sloane.
2022-10-30T18:19:59
oeisdata/seq/A006/A006700.seq
8180b286dc2d93a9606c411ea0b4fe62