Datasets:
christopher
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oeis

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666,262,453B
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-28 00:58:08
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29
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32
32
A006101
Gaussian binomial coefficient [ n,3 ] for q=3.
[ "1", "40", "1210", "33880", "925771", "25095280", "678468820", "18326727760", "494894285941", "13362799477720", "360801469802830", "9741692640081640", "263026177881648511", "7101711092201899360", "191746238094034963240", "5177148775980218655520", "139783020078437440101481" ]
[ "nonn" ]
45
3
2
null
[ "M5272" ]
N. J. A. Sloane
2023-07-14T14:36:41
oeisdata/seq/A006/A006101.seq
76836ee9540bd992647cf985b894afb2
A006102
Gaussian binomial coefficient [ n,4 ] for q=3.
[ "1", "121", "11011", "925771", "75913222", "6174066262", "500777836042", "40581331447162", "3287582741506063", "266307564861468823", "21571273555248777493", "1747282899667791058573", "141530177899268957392924", "11463951511551877750726204", "928580264181940191843785764", "75215006575885931519565302404" ]
[ "nonn" ]
40
4
2
[ "A006102", "A226804" ]
[ "M5384" ]
N. J. A. Sloane
2022-12-31T11:46:13
oeisdata/seq/A006/A006102.seq
3dbe8eebd7ffc6aeecef2d8826921d9a
A006103
Gaussian binomial coefficient [ 2n,n ] for q=3.
[ "1", "4", "130", "33880", "75913222", "1506472167928", "267598665689058580", "427028776969176679964080", "6129263888495201102915629695046", "791614563787525746761491781638123230424", "920094266641283414155073889843358388073398779900" ]
[ "nonn", "easy" ]
30
0
2
[ "A006103", "A022167" ]
[ "M3715" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006103.seq
bbed3c775ce9ed8e818d416f9e96e7fe
A006104
Gaussian binomial coefficient [ n,n/2 ] for q=3.
[ "1", "1", "4", "13", "130", "1210", "33880", "925771", "75913222", "6174066262", "1506472167928", "366573514642546", "267598665689058580", "195168545232713290660", "427028776969176679964080", "934054234760012359481199283", "6129263888495201102915629695046" ]
[ "nonn" ]
20
0
3
null
[ "M3472" ]
N. J. A. Sloane
2018-02-02T02:42:13
oeisdata/seq/A006/A006104.seq
fdbb5d17ed49d15ff78f7fc1e0b84886
A006105
Gaussian binomial coefficient [ n,2 ] for q=4.
[ "1", "21", "357", "5797", "93093", "1490853", "23859109", "381767589", "6108368805", "97734250405", "1563749404581", "25019996065701", "400319959420837", "6405119440211877", "102481911401303973" ]
[ "nonn" ]
52
2
2
null
[ "M5115" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A006/A006105.seq
a76e67e18247924839f2a9777d0eb89d
A006106
Gaussian binomial coefficient [ n,3 ] for q = 4.
[ "1", "85", "5797", "376805", "24208613", "1550842085", "99277752549", "6354157930725", "406672215935205", "26027119554103525", "1665737215212030181", "106607206793565997285", "6822861635108183247077", "436663151052043168024805", "27946441769812674154891493" ]
[ "nonn", "easy" ]
43
3
2
null
[ "M5360" ]
N. J. A. Sloane
2023-07-14T14:39:05
oeisdata/seq/A006/A006106.seq
c1002041e1440bd6af7ed2f7ffa1c09c
A006107
Gaussian binomial coefficient [ n,4 ] for q = 4.
[ "1", "341", "93093", "24208613", "6221613541", "1594283908581", "408235958349285", "104514759495347685", "26756185103024942565", "6849609413493939400165", "1753501675591663698472421", "448896535558672700374937061", "114917519925881846404167134693" ]
[ "nonn", "easy" ]
28
4
2
null
[ "M5445" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006107.seq
904e5107fc533319897059cd11562041
A006108
Gaussian binomial coefficient [ 2n,n ] for q=4.
[ "1", "5", "357", "376805", "6221613541", "1634141006295525", "6857430062381149327845", "460250514083576206796548772325", "494205307747746503853075131001823990245" ]
[ "nonn" ]
11
0
2
null
[ "M4035" ]
N. J. A. Sloane.
2017-11-03T22:14:30
oeisdata/seq/A006/A006108.seq
762f3c239ea19e06b61b32f9d493c324
A006109
Gaussian binomial coefficient [ n,n/2 ] for q=4.
[ "1", "1", "5", "21", "357", "5797", "376805", "24208613", "6221613541", "1594283908581", "1634141006295525", "1673768626404966885", "6857430062381149327845", "28089747579101385828291045", "460250514083576206796548772325", "7540859480106603961931048583270885" ]
[ "nonn" ]
17
0
3
null
[ "M3917" ]
N. J. A. Sloane
2018-02-01T21:18:40
oeisdata/seq/A006/A006109.seq
dc971c504fd8efced0c09b9d2f1a7230
A006110
Gaussian binomial coefficient [ n,5 ] for q = 2.
[ "1", "63", "2667", "97155", "3309747", "109221651", "3548836819", "114429029715", "3675639930963", "117843461817939", "3774561792168531", "120843139740969555", "3867895279362300499", "123787287537281350227", "3961427432158861458003", "126769425631762997934675", "4056681585917103881615955", "129814770207420913565727315" ]
[ "nonn", "easy" ]
53
5
2
[ "A006097", "A006110" ]
[ "M5327" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006110.seq
7820bccf6a187a3d20f25ea2d3495812
A006111
Gaussian binomial coefficient [ n,2 ] for q=5.
[ "1", "31", "806", "20306", "508431", "12714681", "317886556", "7947261556", "198682027181", "4967053120931", "124176340230306", "3104408566792806", "77610214474995931", "1940255363400777181", "48506384092648824056", "1212659602354367574056", "30316490059049924214681" ]
[ "nonn" ]
42
2
2
null
[ "M5228" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A006/A006111.seq
4bba3163502766d8b32d65b88d921ddf
A006112
Gaussian binomial coefficient [ n,3 ] for q = 5.
[ "1", "156", "20306", "2558556", "320327931", "40053706056", "5007031143556", "625886840206056", "78236053707784181", "9779511680526143556", "1222439084242108174806", "152804888634672088643556", "19100611156944225555440431", "2387576396558283557830831056" ]
[ "nonn", "easy" ]
44
3
2
null
[ "M5404" ]
N. J. A. Sloane
2023-07-14T14:40:36
oeisdata/seq/A006/A006112.seq
2f75f71de11940131c9cd56358cb8fe0
A006113
Gaussian binomial coefficient [ n,4 ] for q = 5.
[ "1", "781", "508431", "320327931", "200525284806", "125368356709806", "78360229974772306", "48975769621072897306", "30609934249224268600431", "19131218685276848401412931", "11957012900737114492991256681", "7473133215765585192791624069181", "4670708278954101902438990598678556" ]
[ "nonn", "easy" ]
31
4
2
null
[ "M5479" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006113.seq
c6795558dfd008dbb358d246b28566db
A006114
Gaussian binomial coefficient [ 2n,n ] for q=5.
[ "1", "6", "806", "2558556", "200525284806", "391901483074853556", "19138263752352528498478556", "23362736428829868448189697999416056", "712977784594148279816735342927316866304884806", "543959438081999965602054955428186322207689611643379103556" ]
[ "nonn" ]
25
0
2
null
[ "M4314" ]
N. J. A. Sloane
2018-06-10T11:47:21
oeisdata/seq/A006/A006114.seq
02132ac2437aa71a66dbf2ecc3bab8c4
A006115
Gaussian binomial coefficient [ n,n/2 ] for q=5.
[ "1", "1", "6", "31", "806", "20306", "2558556", "320327931", "200525284806", "125368356709806", "391901483074853556", "1224770494838892134806", "19138263752352528498478556" ]
[ "nonn" ]
16
0
3
null
[ "M4211" ]
N. J. A. Sloane
2018-02-01T21:09:56
oeisdata/seq/A006/A006115.seq
03d313460fe96a9d537c2cf138cb325a
A006116
Sum of Gaussian binomial coefficients [n,k] for q=2 and k=0..n.
[ "1", "2", "5", "16", "67", "374", "2825", "29212", "417199", "8283458", "229755605", "8933488744", "488176700923", "37558989808526", "4073773336877345", "623476476706836148", "134732283882873635911", "41128995468748254231002", "17741753171749626840952685", "10817161765507572862559462656" ]
[ "nonn", "easy", "nice" ]
105
0
2
[ "A005329", "A006116", "A006516", "A022166", "A083906" ]
[ "M1501" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006116.seq
25696cb1b2a64442e5dcaeac89a29660
A006117
Sum of Gaussian binomial coefficients [ n,k ] for q=3.
[ "1", "2", "6", "28", "212", "2664", "56632", "2052656", "127902864", "13721229088", "2544826627424", "815300788443072", "452436459318538048", "434188323928823259776", "722197777341507864283008", "2078153254879878944892861184", "10366904326991986000747424911616", "89478415088556766546699920236339712", "1338962661056423158371347974009398601216" ]
[ "nonn", "easy" ]
45
0
2
null
[ "M1687" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006117.seq
81b71cdd3dce85b6ba3253b18ad8b0f0
A006118
Sum of Gaussian binomial coefficients [ n,k ] for q=4.
[ "1", "2", "7", "44", "529", "12278", "565723", "51409856", "9371059621", "3387887032202", "2463333456292207", "3557380311703796564", "10339081666350180289849", "59703612489554311631068958" ]
[ "nonn" ]
35
0
2
[ "A006118", "A022168" ]
[ "M1812" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006118.seq
ea1c2e551bfab3baaf751e6913195604
A006119
Sum of Gaussian binomial coefficients [ n,k ] for q=5.
[ "1", "2", "8", "64", "1120", "42176", "3583232", "666124288", "281268665344", "260766671206400", "549874114073747456", "2547649010961476288512", "26854416724405008878829568" ]
[ "nonn" ]
36
0
2
[ "A006119", "A022169" ]
[ "M1898" ]
N. J. A. Sloane
2024-05-23T15:11:37
oeisdata/seq/A006/A006119.seq
ec7d29a16c7fead9289f92f709607233
A006120
Sum of Gaussian binomial coefficients [ n,k ] for q=6.
[ "1", "2", "9", "88", "2111", "118182", "16649389", "5547079988", "4671840869691", "9326302435784002", "47100039978152210249", "564020035264998031552848", "17088883834526416216141122391", "1227783027118593811726444427584862", "223195138386683651821176756496371359589" ]
[ "nonn", "easy" ]
27
0
2
null
[ "M1952" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006120.seq
6805a459d6f2b39d20e8a141d2af6793
A006121
Sum of Gaussian binomial coefficients [ n,k ] for q=7.
[ "1", "2", "10", "116", "3652", "285704", "61946920", "33736398032", "51083363186704", "194585754101247008", "2061787082699360148640", "54969782721182164414355264" ]
[ "nonn" ]
28
0
2
null
[ "M1984" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006121.seq
c09d4ba0ed0d66bd9658a8a9b3b6233c
A006122
Sum of Gaussian binomial coefficients [ n,k ] for q=8.
[ "1", "2", "11", "148", "5917", "617894", "195118127", "162366823096", "409516908802369", "2724882133766162378", "54969878431787791720019", "2925929849527072623051175132", "472193512063977840212540697627493", "201069312609841845828101079279279809006" ]
[ "easy", "nonn" ]
28
0
2
null
[ "M2010" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006122.seq
55b773114b6e92909d958b1cf9399463
A006123
Erroneous version of A000085.
[ "1", "1", "2", "4", "10", "26", "75", "215" ]
[ "dead" ]
21
0
3
null
[ "M1215" ]
Colin Mallows
2018-03-08T03:47:52
oeisdata/seq/A006/A006123.seq
143b2d1f25578c537a722ed2146ea870
A006124
a(n) = 3 + n/2 + 7*n^2/2.
[ "3", "7", "18", "36", "61", "93", "132", "178", "231", "291", "358", "432", "513", "601", "696", "798", "907", "1023", "1146", "1276", "1413", "1557", "1708", "1866", "2031", "2203", "2382", "2568", "2761", "2961", "3168", "3382", "3603", "3831", "4066", "4308", "4557", "4813", "5076", "5346", "5623", "5907", "6198", "6496", "6801", "7113", "7432", "7758" ]
[ "nonn", "easy" ]
38
0
1
[ "A006124", "A022265" ]
null
N. J. A. Sloane
2024-12-30T14:56:58
oeisdata/seq/A006/A006124.seq
adf8533233d5c4b63a896930fbe1603d
A006125
a(n) = 2^(n*(n-1)/2).
[ "1", "1", "2", "8", "64", "1024", "32768", "2097152", "268435456", "68719476736", "35184372088832", "36028797018963968", "73786976294838206464", "302231454903657293676544", "2475880078570760549798248448", "40564819207303340847894502572032", "1329227995784915872903807060280344576" ]
[ "nonn", "easy", "nice" ]
242
0
3
[ "A000088", "A000169", "A000295", "A000568", "A001187", "A002416", "A002494", "A004003", "A005329", "A006125", "A006129", "A006253", "A016031", "A036442", "A053763", "A058891", "A059167", "A095340", "A100743", "A103904", "A114604", "A136284", "A136652", "A143543", "A158474", "A287689", "A299998", "A327078" ]
[ "M1897" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006125.seq
6b62fe51511cb431b5c8a58627fd5f18
A006126
Number of hierarchical models on n labeled factors or variables with linear terms forced. Also number of antichain covers of a labeled n-set.
[ "2", "1", "2", "9", "114", "6894", "7785062", "2414627396434", "56130437209370320359966", "286386577668298410623295216696338374471993" ]
[ "nonn", "nice", "hard", "more" ]
136
0
1
[ "A000372", "A006126", "A006602", "A014466", "A051112", "A051118", "A056046", "A056049", "A056052", "A056101", "A056104", "A261005", "A293606", "A293993", "A305000", "A305844", "A306550", "A307249", "A317674", "A319721", "A320449" ]
[ "M1954" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006126.seq
4547ae4f6473162b1e9ef754a3066580
A006127
a(n) = 2^n + n.
[ "1", "3", "6", "11", "20", "37", "70", "135", "264", "521", "1034", "2059", "4108", "8205", "16398", "32783", "65552", "131089", "262162", "524307", "1048596", "2097173", "4194326", "8388631", "16777240", "33554457", "67108890", "134217755", "268435484", "536870941", "1073741854", "2147483679", "4294967328", "8589934625" ]
[ "nonn", "easy" ]
122
0
2
[ "A000051", "A000079", "A000325", "A006127", "A052944", "A135227" ]
[ "M2547" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006127.seq
6ed8a79850fce64e03a1c04f36aae9cd
A006128
Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n.
[ "0", "1", "3", "6", "12", "20", "35", "54", "86", "128", "192", "275", "399", "556", "780", "1068", "1463", "1965", "2644", "3498", "4630", "6052", "7899", "10206", "13174", "16851", "21522", "27294", "34545", "43453", "54563", "68135", "84927", "105366", "130462", "160876", "198014", "242812", "297201", "362587", "441546", "536104", "649791", "785437", "947812", "1140945", "1371173", "1644136", "1968379", "2351597", "2805218", "3339869", "3970648", "4712040", "5584141", "6606438", "7805507", "9207637" ]
[ "nonn", "easy", "nice" ]
246
0
3
[ "A000005", "A000041", "A000070", "A001787", "A001792", "A006128", "A008284", "A015723", "A046746", "A066186", "A066633", "A066637", "A083710", "A085410", "A093694", "A130689", "A209423", "A210485", "A256193", "A264401", "A276024", "A285220", "A336875", "A336902", "A336903", "A339564", "A343341" ]
[ "M2552" ]
N. J. A. Sloane, Colin Mallows
2025-02-16T08:32:29
oeisdata/seq/A006/A006128.seq
3d3e22cd047bc3187cbca44a107d7930
A006129
a(0), a(1), a(2), ... satisfy Sum_{k=0..n} a(k)*binomial(n,k) = 2^binomial(n,2), for n >= 0.
[ "1", "0", "1", "4", "41", "768", "27449", "1887284", "252522481", "66376424160", "34509011894545", "35645504882731588", "73356937912127722841", "301275024444053951967648", "2471655539737552842139838345", "40527712706903544101000417059892", "1328579255614092968399503598175745633" ]
[ "nonn", "nice", "easy" ]
74
0
4
[ "A002494", "A006129", "A054548", "A086193", "A322661" ]
[ "M3678" ]
Colin Mallows
2025-02-16T08:32:29
oeisdata/seq/A006/A006129.seq
34cd29f32b1cf1b0935ebb6f9f39d25f
A006130
a(n) = a(n-1) + 3*a(n-2) for n > 1, a(0) = a(1) = 1.
[ "1", "1", "4", "7", "19", "40", "97", "217", "508", "1159", "2683", "6160", "14209", "32689", "75316", "173383", "399331", "919480", "2117473", "4875913", "11228332", "25856071", "59541067", "137109280", "315732481", "727060321", "1674257764", "3855438727", "8878212019", "20444528200" ]
[ "nonn", "easy" ]
280
0
3
[ "A006130", "A006131", "A015440", "A049310", "A052533", "A099232", "A140167", "A175291", "A209927", "A274977", "A356033" ]
[ "M3314" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006130.seq
b7ff66cb4f780392ea19100d4795878d
A006131
a(n) = a(n-1) + 4*a(n-2), a(0) = a(1) = 1.
[ "1", "1", "5", "9", "29", "65", "181", "441", "1165", "2929", "7589", "19305", "49661", "126881", "325525", "833049", "2135149", "5467345", "14007941", "35877321", "91909085", "235418369", "603054709", "1544728185", "3956947021", "10135859761", "25963647845", "66507086889", "170361678269" ]
[ "nonn", "easy" ]
179
0
3
[ "A006130", "A006131", "A015440", "A026581", "A026583", "A026597", "A026599", "A052923", "A063727", "A097705", "A102446", "A344236", "A344261" ]
[ "M3788" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006131.seq
9a49044301ba627927cb84f655f7b38c
A006132
Related to representations as sums of Fibonacci numbers.
[ "1", "6", "9", "22", "40", "43", "48", "56", "61", "64", "111", "145", "150", "153", "166", "255", "273", "276", "281", "289", "294", "297", "310", "315", "318", "323", "328", "331", "336", "344", "378", "383", "386", "399", "417", "420", "425", "433", "438", "441", "488", "721", "755", "760", "763", "776", "865", "988", "993", "996", "1009", "1027", "1030", "1035" ]
[ "nonn" ]
16
1
2
null
[ "M4079" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A006/A006132.seq
2bc7b0df56ca62fd2ccede0b3a2a3e9b
A006133
Related to representations as sums of Fibonacci numbers.
[ "3", "21", "32", "79", "144", "155", "173", "202", "220", "231", "401", "524", "542", "553", "600", "922", "987", "998", "1016", "1045", "1063", "1074", "1121", "1139", "1150", "1168", "1186", "1197", "1215", "1244", "1367", "1385", "1396", "1443", "1508", "1519", "1537", "1566", "1584", "1595", "1765", "2608", "2731", "2749", "2760", "2807", "3129" ]
[ "nonn" ]
18
1
1
null
[ "M3080" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A006/A006133.seq
73a305e8026e5638faa8ce267b45ad41
A006134
a(n) = Sum_{k=0..n} binomial(2*k,k).
[ "1", "3", "9", "29", "99", "351", "1275", "4707", "17577", "66197", "250953", "956385", "3660541", "14061141", "54177741", "209295261", "810375651", "3143981871", "12219117171", "47564380971", "185410909791", "723668784231", "2827767747951", "11061198475551", "43308802158651", "169719408596403", "665637941544507" ]
[ "nonn" ]
170
0
2
[ "A000975", "A000984", "A006134", "A006135", "A006136", "A007318", "A013580", "A024718", "A038874", "A045912", "A057552", "A066796", "A079309", "A097933", "A100066", "A132310", "A231147", "A327481", "A359893", "A359901", "A361654" ]
[ "M2811" ]
N. J. A. Sloane
2025-03-21T09:33:42
oeisdata/seq/A006/A006134.seq
3b4fa4f45431c3254481ae3e9197393c
A006135
T(n+2,2) from table A045912 of characteristic polynomial of negative Pascal matrix.
[ "1", "9", "72", "626", "6084", "64974", "744193", "8965323", "112088583", "1441465015", "18952951005", "253712542005", "3447133563343", "47425573790397", "659506609478472", "9256644358552742", "130981854694547790", "1866712391002772586" ]
[ "nonn", "easy" ]
23
0
2
[ "A006134", "A006135", "A006136", "A045912" ]
[ "M4650" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A006/A006135.seq
e52d2e1b63fe80779dab1b928310e0c0
A006136
T(n+3,3) from table A045912 of characteristic polynomial of negative Pascal matrix.
[ "1", "29", "626", "13869", "347020", "9952274", "321541977", "11416400590", "435869304863", "17605464402686", "743624059688891", "32572923621373010", "1470621027107356485", "68120063089374617281", "3225635202844511176442", "155695310201341829770911" ]
[ "nonn" ]
18
0
2
[ "A006134", "A006135", "A006136", "A045912" ]
[ "M5206" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A006/A006136.seq
843fe23d50e7ac60f85e5ed4696269c7
A006137
a(n) = 1 + n/2 + 9*n^2/2.
[ "1", "6", "20", "43", "75", "116", "166", "225", "293", "370", "456", "551", "655", "768", "890", "1021", "1161", "1310", "1468", "1635", "1811", "1996", "2190", "2393", "2605", "2826", "3056", "3295", "3543", "3800", "4066", "4341", "4625", "4918", "5220", "5531", "5851", "6180", "6518", "6865", "7221", "7586", "7960", "8343", "8735", "9136", "9546" ]
[ "nonn", "easy" ]
46
0
2
[ "A002378", "A003215", "A006137", "A161705", "A276819" ]
null
N. J. A. Sloane
2024-02-19T01:49:00
oeisdata/seq/A006/A006137.seq
3803ec5cdebadeef266710b535445bf9
A006138
a(n) = a(n-1) + 3*a(n-2).
[ "1", "2", "5", "11", "26", "59", "137", "314", "725", "1667", "3842", "8843", "20369", "46898", "108005", "248699", "572714", "1318811", "3036953", "6993386", "16104245", "37084403", "85397138", "196650347", "452841761", "1042792802", "2401318085", "5529696491", "12733650746", "29322740219", "67523692457", "155491913114" ]
[ "nonn", "easy" ]
80
0
2
[ "A006130", "A006138", "A006190", "A016116", "A063782", "A105476", "A122950", "A175654", "A274977" ]
[ "M1399" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006138.seq
c21e3f8ef39f4314b1984d45977fd0b3
A006139
n*a(n) = 2*(2*n-1)*a(n-1) + 4*(n-1)*a(n-2) with a(0) = 1.
[ "1", "2", "8", "32", "136", "592", "2624", "11776", "53344", "243392", "1116928", "5149696", "23835904", "110690816", "515483648", "2406449152", "11258054144", "52767312896", "247736643584", "1164829376512", "5484233814016", "25852072517632", "121997903495168" ]
[ "nonn", "easy" ]
104
0
2
[ "A001850", "A002426", "A006139", "A036442", "A084600", "A084606", "A084608", "A084615", "A106258", "A106259", "A106260", "A106261", "A110446", "A123178" ]
[ "M1849" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006139.seq
8011b23579864c56dfd4194c9401e3ce
A006140
Erroneous version of A003406.
[ "1", "1", "-2", "2", "-2", "1", "0", "1", "-2", "0", "2", "0", "-1", "-2", "2", "1", "0", "-2", "2", "-2" ]
[ "dead" ]
4
0
3
null
null
null
1999-12-11T03:00:00
oeisdata/seq/A006/A006140.seq
7b5db7acf3af3a3049d178d5e7bfc2ef
A006141
Number of integer partitions of n whose smallest part is equal to the number of parts.
[ "1", "0", "0", "1", "1", "1", "1", "1", "2", "2", "3", "3", "4", "4", "5", "6", "7", "8", "10", "11", "13", "15", "17", "19", "23", "25", "29", "33", "38", "42", "49", "54", "62", "69", "78", "87", "99", "109", "123", "137", "154", "170", "191", "211", "236", "261", "290", "320", "357", "392", "435", "479", "530", "582", "644", "706", "779", "854", "940", "1029", "1133", "1237", "1358", "1485" ]
[ "nonn" ]
136
1
9
[ "A003106", "A003113", "A003114", "A006141", "A010054", "A026794", "A039899", "A039900", "A047993", "A055396", "A064174", "A090858", "A098124", "A106529", "A114638", "A117409", "A239950", "A264591", "A264592", "A264593", "A264594", "A264595", "A324516", "A324518", "A324520", "A324522", "A325134", "A340596", "A340598", "A340599", "A340600", "A340601", "A340611", "A340653", "A340654", "A340655" ]
[ "M0260" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006141.seq
6d7a6a2f88e6efae53acf894bf8c33ea
A006142
Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).
[ "0", "0", "0", "0", "0", "1", "0", "1", "7", "17", "30", "49", "124", "321", "761", "1721", "3815" ]
[ "nonn", "walk" ]
14
4
9
[ "A002976", "A006142" ]
[ "M4355" ]
N. J. A. Sloane
2018-12-27T07:57:34
oeisdata/seq/A006/A006142.seq
57cfea053a3d723ad7309b93819ec446
A006143
Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).
[ "0", "0", "0", "1", "0", "0", "2", "7", "12", "14", "36", "95", "226", "501", "1056", "2377", "5448" ]
[ "nonn", "walk", "more" ]
15
4
7
[ "A002976", "A006143" ]
[ "M1737" ]
N. J. A. Sloane
2018-12-27T07:57:41
oeisdata/seq/A006/A006143.seq
f82ea4a4f7cb9103bf63c31c44aced40
A006144
Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).
[ "0", "1", "0", "0", "0", "4", "5", "6", "11", "31", "72", "157", "312", "700", "1472", "3446", "7855" ]
[ "walk", "nonn", "more" ]
14
4
6
[ "A002976", "A006144" ]
[ "M3242" ]
N. J. A. Sloane
2018-12-27T07:57:49
oeisdata/seq/A006/A006144.seq
8c24f92a4b3a7b66512540f99256bb97
A006145
Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1.
[ "5", "24", "49", "77", "104", "153", "369", "492", "714", "1682", "2107", "2299", "2600", "2783", "5405", "6556", "6811", "8855", "9800", "12726", "13775", "18655", "21183", "24024", "24432", "24880", "25839", "26642", "35456", "40081", "43680", "48203", "48762", "52554", "61760", "63665", "64232", "75140", "79118", "95709", "106893", "109939" ]
[ "nonn" ]
79
1
1
[ "A006145", "A006146", "A039752", "A039753", "A054378" ]
null
N. J. A. Sloane
2025-03-13T12:10:40
oeisdata/seq/A006/A006145.seq
9af2762d714f5df7d4aa62b9be07a2fe
A006146
Sums of prime divisors of Ruth-Aaron numbers (A006145).
[ "5", "5", "7", "18", "15", "20", "44", "46", "29", "31", "50", "30", "20", "34", "75", "162", "146", "46", "14", "113", "53", "66", "333", "36", "514", "318", "43", "193", "279", "418", "30", "121", "55", "485", "200", "136", "77", "37", "211", "587", "147", "269", "477", "108", "136", "235", "185", "290", "333", "309", "493", "177", "199", "223", "641", "531", "182", "368" ]
[ "nonn" ]
35
1
1
[ "A006145", "A006146", "A008472", "A039703", "A039752", "A039753", "A054378" ]
null
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006146.seq
2e9c930ce58e9247274d3de75a2c86d4
A006147
Reversion of Ramanujan numbers.
[ "1", "24", "900", "40352", "1994322", "104816880", "5747466920", "325077729600", "18826860841119", "1110900168420264", "66547088543789532", "4036419643768799328", "247405021070280491110", "15299980644645295780560", "953473460271200881693560", "59817824263728235912396224" ]
[ "nonn" ]
18
1
2
[ "A000594", "A006147" ]
null
N. J. A. Sloane
2025-01-07T01:58:26
oeisdata/seq/A006/A006147.seq
ea4113aa64abd70b25d24b5d49b259bc
A006148
Number of 4 X n binary matrices up to row and column permutations.
[ "1", "5", "22", "87", "317", "1053", "3250", "9343", "25207", "64167", "155004", "357009", "787586", "1670643", "3419552", "6774765", "13027340", "24372942", "44462456", "79240762", "138204782", "236258358", "396409924", "653639898", "1060379169", "1694174350", "2668300758", "4146300078", "6361709115", "9644583474" ]
[ "nonn", "nice", "easy" ]
53
0
2
[ "A002623", "A002727", "A006148", "A006380", "A028657" ]
[ "M3919" ]
N. J. A. Sloane
2025-03-07T12:06:11
oeisdata/seq/A006/A006148.seq
8a05aa6d056d4707302bc1e26f09f831
A006149
Number of 3-tuples (p_1, p_2, p_3) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.
[ "1", "1", "4", "30", "330", "4719", "81796", "1643356", "37119160", "922268360", "24801924512", "713055329720", "21706243125300", "694280570551875", "23188541161342500", "804601696647424500", "28880966163870711000", "1068595748063216307000", "40631980618055892780000", "1583603339463794983230000" ]
[ "nonn", "easy" ]
70
0
3
[ "A000108", "A005700", "A006149", "A006150", "A006151", "A078920", "A123352", "A185249" ]
[ "M3634" ]
N. J. A. Sloane, Simon Plouffe
2024-09-20T04:14:17
oeisdata/seq/A006/A006149.seq
f72bf2aa7b96931a8352771b2da83a3a
A006150
Number of 4-tuples (p_1, p_2, ..., p_4) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.
[ "1", "1", "5", "55", "1001", "26026", "884884", "37119160", "1844536720", "105408179176", "6774025632340", "481155055944150", "37259723952950625", "3111129272480118750", "277587585343361452500", "26268551497229678505000", "2620002484114994890890000", "273961129317241857069150000", "29896847445736985488399170000" ]
[ "nonn", "easy" ]
69
0
3
[ "A000108", "A005700", "A006149", "A006150", "A006151", "A078920", "A123352", "A185249" ]
[ "M4013" ]
N. J. A. Sloane
2024-09-20T04:14:35
oeisdata/seq/A006/A006150.seq
00c64ceecd16dcf60f673d25f5c62d7d
A006151
Number of 5-tuples (p_1, p_2, ..., p_5) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.
[ "1", "1", "6", "91", "2548", "111384", "6852768", "553361016", "55804330152", "6774025632340", "962310111888300", "156490840602392625", "28622389306817092500", "5804104057179375825000", "1289547073500366035700000", "310827567433642575691950000", "80604345356574686019872460000" ]
[ "nonn", "easy" ]
57
0
3
[ "A000108", "A005700", "A006149", "A006150", "A006151", "A078920", "A123352", "A185249" ]
[ "M4288" ]
N. J. A. Sloane
2024-09-20T04:16:15
oeisdata/seq/A006/A006151.seq
2d53b53f1a69ecc90e16df90c072fd58
A006152
Exponential generating function x*exp(x/(1-x)).
[ "1", "2", "9", "52", "365", "3006", "28357", "301064", "3549177", "45965530", "648352001", "9888877692", "162112109029", "2841669616982", "53025262866045", "1049180850990736", "21937381717388657", "483239096122434354", "11184035897992673017", "271287473871771163460", "6881656485607798743261" ]
[ "nonn", "easy" ]
54
1
2
[ "A000262", "A006152", "A320264" ]
[ "M1939" ]
Simon Plouffe
2024-09-19T18:07:55
oeisdata/seq/A006/A006152.seq
02035ee55cfc0b319ae7ef8b6b4995af
A006153
E.g.f.: 1/(1-x*exp(x)).
[ "1", "1", "4", "21", "148", "1305", "13806", "170401", "2403640", "38143377", "672552730", "13044463641", "276003553860", "6326524990825", "156171026562838", "4130464801497105", "116526877671782896", "3492868475952497313", "110856698175372359346", "3713836169709782989993", "130966414749485504586940" ]
[ "nonn", "easy", "nice" ]
83
0
3
[ "A003566", "A006153", "A072597", "A089148", "A199673" ]
[ "M3578" ]
Simon Plouffe and N. J. A. Sloane
2022-03-09T10:27:04
oeisdata/seq/A006/A006153.seq
fa96cdbd762c2a14013e650ff5478fa7
A006154
Number of labeled ordered partitions of an n-set into odd parts.
[ "1", "1", "2", "7", "32", "181", "1232", "9787", "88832", "907081", "10291712", "128445967", "1748805632", "25794366781", "409725396992", "6973071372547", "126585529106432", "2441591202059281", "49863806091395072", "1074927056650469527", "24392086908129247232", "581176736647853024581" ]
[ "nonn", "easy", "nice" ]
91
0
3
[ "A000045", "A000111", "A000670", "A003724", "A006154", "A193474", "A196776" ]
[ "M1792" ]
Simon Plouffe
2024-12-29T00:42:44
oeisdata/seq/A006/A006154.seq
a23bffe6f25fb3caa2aa6760abd3107c
A006155
Expansion of e.g.f.: 1/(2-x-exp(x)).
[ "1", "2", "9", "61", "551", "6221", "84285", "1332255", "24066691", "489100297", "11044268633", "274327080611", "7433424980943", "218208342366093", "6898241919264181", "233651576126946103", "8441657595745501019", "324052733365292875025", "13171257161208184782225", "565092918793429218839307" ]
[ "nonn", "easy" ]
31
0
2
[ "A006155", "A032112" ]
[ "M1945" ]
Simon Plouffe
2025-01-09T05:31:42
oeisdata/seq/A006/A006155.seq
7e08fa68d1c1f2101c209be08776279e
A006156
Number of ternary squarefree words of length n.
[ "1", "3", "6", "12", "18", "30", "42", "60", "78", "108", "144", "204", "264", "342", "456", "618", "798", "1044", "1392", "1830", "2388", "3180", "4146", "5418", "7032", "9198", "11892", "15486", "20220", "26424", "34422", "44862", "58446", "76122", "99276", "129516", "168546", "219516", "285750", "372204", "484446", "630666", "821154" ]
[ "nonn", "nice" ]
99
0
2
[ "A006156", "A060688", "A215075", "A282212" ]
[ "M2550" ]
N. J. A. Sloane, Jeffrey Shallit, Doron Zeilberger
2025-02-16T08:32:29
oeisdata/seq/A006/A006156.seq
08a3b039023e5b8f308b35625b475086
A006157
a(n+1) = (n-1)*a(n) + n*n!.
[ "1", "5", "28", "180", "1320", "10920", "100800", "1028160", "11491200", "139708800", "1836172800", "25945920000", "392302310400", "6320426112000", "108101081088000", "1956280854528000", "37347179950080000", "750144785854464000", "15813863053148160000", "349121438173347840000" ]
[ "nonn", "easy" ]
33
2
2
[ "A006157", "A014484" ]
[ "M3950" ]
N. J. A. Sloane, Simon Plouffe
2025-01-09T08:02:40
oeisdata/seq/A006/A006157.seq
7aec410560f3bfc1ecb5c3961b6f165b
A006158
a(n) = a(a(n-3)) + a(n-a(n-3)).
[ "1", "1", "1", "2", "3", "4", "4", "4", "5", "6", "6", "7", "8", "8", "8", "8", "9", "10", "10", "11", "12", "13", "13", "14", "15", "16", "16", "16", "16", "16", "16", "16", "17", "18", "18", "19", "20", "21", "21", "22", "23", "24", "25", "25", "26", "27", "28", "29", "29", "29", "29", "29", "30", "31", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "33", "34", "34", "35", "36", "37", "37", "38", "39", "40", "41" ]
[ "nonn" ]
20
1
4
null
[ "M0447" ]
N. J. A. Sloane.
2018-10-24T10:54:12
oeisdata/seq/A006/A006158.seq
2f82a6fbce7cd4e2df79b2ba4bf0145f
A006159
a(n)=a(a(n-4))+a(n-a(n-4)).
[ "1", "1", "1", "1", "2", "3", "4", "5", "5", "5", "5", "6", "7", "7", "7", "8", "9", "9", "10", "11", "11", "12", "12", "12", "12", "13", "13", "14", "15", "16", "16", "16", "16", "17", "18", "19", "19", "20", "20", "21", "22", "23", "23", "23", "24", "24", "24", "24", "24", "25", "25", "26", "27", "27", "28", "29" ]
[ "nonn" ]
8
1
5
null
[ "M0454" ]
N. J. A. Sloane.
2012-03-30T16:44:55
oeisdata/seq/A006/A006159.seq
2885c81cf199a3d8037bca02bd5b1cd7
A006160
a(n)=a(a(n-5))+a(n-a(n-5)).
[ "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "6", "6", "6", "6", "7", "8", "8", "8", "8", "9", "10", "10", "11", "12", "13", "14", "14", "14", "14", "14", "14", "14", "14", "15", "16", "16", "17", "18", "19", "20", "21", "21", "21", "21", "22", "23", "24", "24", "24", "24", "25", "26", "26", "26", "26", "27", "28", "28", "28", "29", "29", "29", "30", "30", "30", "31", "32", "32", "33", "34", "34", "34", "35", "35", "36", "36" ]
[ "nonn", "easy" ]
8
1
6
null
[ "M0463" ]
N. J. A. Sloane.
2012-03-30T16:44:55
oeisdata/seq/A006/A006160.seq
6f52770101fcb2010cb5aea5e7325dd5
A006161
a(n)=a(a(n-1)-1)+a(n+1-a(n-1)).
[ "1", "1", "2", "3", "3", "4", "5", "6", "6", "6", "7", "8", "9", "10", "10", "11", "11", "12", "13", "14", "15", "16", "16", "16", "16", "17", "18", "18", "19", "20", "21", "22", "23", "24", "24", "25", "25", "26", "26", "26", "27", "28", "29", "29", "29", "30", "31", "32", "33", "34", "35", "36", "36", "37", "38", "38", "39", "40", "40", "41", "41", "42", "43", "44", "45", "45", "45", "45", "45", "46", "46", "47", "48", "49" ]
[ "nonn", "easy" ]
8
1
3
null
[ "M0440" ]
N. J. A. Sloane.
2012-03-30T16:44:55
oeisdata/seq/A006/A006161.seq
ad41aaf7face9a6404a1edfbe33164bd
A006162
a(n)=a(a(n-1)-2)+a(n+2-a(n-1)).
[ "1", "1", "2", "3", "4", "4", "5", "6", "7", "8", "8", "8", "9", "10", "11", "12", "13", "13", "14", "14", "15", "16", "17", "18", "19", "20", "20", "21", "22", "22", "22", "22", "23", "24", "25", "26", "27", "28", "29", "29", "30", "31", "32", "32", "33", "33", "34", "34", "35", "36", "37", "38", "39", "40", "41" ]
[ "nonn" ]
8
1
3
null
[ "M0450" ]
N. J. A. Sloane.
2012-03-30T16:44:55
oeisdata/seq/A006/A006162.seq
6e337c3df065b6f52e5ddaac4f5d9648
A006163
a(n)=a(a(n-1)-3)+a(n+3-a(n-1)).
[ "1", "1", "2", "3", "4", "5", "5", "6", "7", "8", "9", "10", "10", "10", "11", "12", "13", "14", "15", "16", "16", "17", "17", "18", "19", "20", "21", "22", "23", "24", "24", "25", "26", "26", "27", "28", "29", "30", "31", "32", "33", "34", "34", "34", "34", "35", "36", "37", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "46", "47", "47", "48", "48", "49", "50", "51", "52", "52", "53", "54", "55", "56", "57" ]
[ "nonn", "easy" ]
8
1
3
null
[ "M0460" ]
N. J. A. Sloane.
2012-03-30T16:44:55
oeisdata/seq/A006/A006163.seq
4c9d0d594d68c71edb8f782aa2e81a11
A006164
a(n)=a(a(n-1)-4)+a(n+4-a(n-1)).
[ "1", "1", "2", "3", "4", "5", "6", "6", "7", "8", "9", "10", "11", "12", "12", "12", "13", "14", "15", "16", "17", "18", "19", "19", "20", "20", "21", "22", "23", "24", "25", "26", "27", "28", "28", "29", "30", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "39", "40", "41", "42", "42", "42", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "52", "53", "54", "55", "56", "56", "57", "57", "58" ]
[ "nonn", "easy" ]
8
1
3
null
[ "M0465" ]
N. J. A. Sloane.
2012-03-30T16:44:55
oeisdata/seq/A006/A006164.seq
a34e1488d690fb38ee1300b6f544f910
A006165
a(1) = a(2) = 1; thereafter a(2n+1) = a(n+1) + a(n), a(2n) = 2a(n).
[ "1", "1", "2", "2", "3", "4", "4", "4", "5", "6", "7", "8", "8", "8", "8", "8", "9", "10", "11", "12", "13", "14", "15", "16", "16", "16", "16", "16", "16", "16", "16", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43" ]
[ "nonn", "easy" ]
93
1
3
[ "A006165", "A053644", "A060973", "A066997", "A078881" ]
[ "M0277" ]
N. J. A. Sloane
2024-12-29T00:42:37
oeisdata/seq/A006/A006165.seq
5196355dab8cf653b4810e05cc402b33
A006166
a(0)=0, a(1)=a(2)=1; for n >= 1, a(3n+2) = 2a(n+1) + a(n), a(3n+1) = a(n+1) + 2a(n), a(3n) = 3a(n).
[ "0", "1", "1", "3", "3", "3", "3", "5", "7", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "11", "13", "15", "17", "19", "21", "23", "25", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "27", "29", "31", "33", "35", "37", "39", "41", "43", "45", "47", "49", "51", "53", "55", "57", "59", "61", "63", "65", "67", "69" ]
[ "nonn", "easy" ]
25
0
4
[ "A003605", "A006165", "A006166", "A080678", "A081134" ]
[ "M2270" ]
N. J. A. Sloane
2022-10-13T07:50:49
oeisdata/seq/A006/A006166.seq
c7fc0fe4673568181d048d11bf411a52
A006167
Number of factorization patterns of polynomials of degree n over F_2.
[ "1", "3", "4", "8", "11", "20", "27", "45", "61", "95", "128", "193", "257", "374", "497", "703", "927", "1287", "1683", "2297", "2987", "4013", "5186", "6887", "8843", "11614", "14836", "19294", "24514", "31622", "39968", "51167", "64377", "81839", "102509", "129528", "161539", "202959", "252124", "315110", "389949", "485062" ]
[ "nonn", "nice" ]
26
1
2
[ "A001037", "A006167", "A006168", "A006169", "A006170", "A006171" ]
[ "M2349" ]
N. J. A. Sloane
2017-11-03T22:18:25
oeisdata/seq/A006/A006167.seq
7e3d135ecbff965e89c56f32efa99186
A006168
Number of factorization patterns of polynomials of degree n over F_3.
[ "1", "3", "5", "10", "15", "29", "42", "72", "107", "170", "246", "383", "542", "810", "1145", "1662", "2311", "3305", "4537", "6363", "8677", "11974", "16159", "22068", "29504", "39811", "52887", "70632", "93102", "123362", "161473", "212198", "276185", "360270", "466090", "604267", "777399", "1001656", "1282456" ]
[ "nonn" ]
16
1
2
[ "A006167", "A006168", "A006171", "A027376" ]
[ "M2461" ]
N. J. A. Sloane.
2017-11-04T00:27:17
oeisdata/seq/A006/A006168.seq
07c48426c9b51aafe726315f3065e61b
A006169
Number of factorization patterns of polynomials of degree n over F_4.
[ "1", "3", "5", "11", "16", "32", "47", "84", "124", "206", "299", "481", "687", "1058", "1506", "2255", "3163", "4638", "6444", "9258", "12757", "18021", "24604", "34307", "46445", "63926", "85948", "117021", "156156", "210617", "279202", "373252", "491801", "652264", "854343", "1125152", "1465587", "1917282", "2484733" ]
[ "nonn" ]
17
1
2
[ "A006167", "A006169", "A006171", "A027377" ]
[ "M2475" ]
N. J. A. Sloane.
2017-11-04T00:25:53
oeisdata/seq/A006/A006169.seq
80e34e83d219ea1bc8ee87c821e7ace5
A006170
Number of factorization patterns of polynomials of degree n over F_5.
[ "1", "3", "5", "11", "17", "33", "50", "89", "135", "223", "332", "531", "776", "1194", "1730", "2591", "3700", "5429", "7660", "11035", "15417", "21851", "30225", "42300", "57966", "80146", "108956", "149076", "201073", "272587", "365009", "490656", "652700", "870597", "1150875", "1524479", "2003426", "2636589", "3446140" ]
[ "nonn" ]
17
1
2
[ "A001692", "A006167", "A006170", "A006171" ]
[ "M2478" ]
N. J. A. Sloane.
2017-11-04T00:25:21
oeisdata/seq/A006/A006170.seq
0baaae90742c31da9672773ce40ea163
A006171
Number of factorization patterns of polynomials of degree n over integers.
[ "1", "1", "3", "5", "11", "17", "34", "52", "94", "145", "244", "370", "603", "899", "1410", "2087", "3186", "4650", "6959", "10040", "14750", "21077", "30479", "43120", "61574", "86308", "121785", "169336", "236475", "326201", "451402", "618135", "848209", "1153733", "1571063", "2123325", "2871419", "3857569", "5182999", "6924303" ]
[ "nonn", "nice" ]
101
0
3
[ "A000005", "A000041", "A000219", "A001970", "A006167", "A006170", "A006171", "A060640", "A061255", "A061256", "A061257", "A115621", "A215905", "A215909", "A215914", "A215925", "A288098" ]
[ "M2479" ]
N. J. A. Sloane
2024-07-26T11:39:37
oeisdata/seq/A006/A006171.seq
5c97c68143b5d4c6ccd24d2a2c29051a
A006172
a(n) = 1 + F(2*n+1) + (-1)^n*L(n).
[ "4", "2", "9", "10", "42", "79", "252", "582", "1645", "4106", "11070", "28459", "75348", "195898", "515073", "1344906", "3526786", "9223895", "24163596", "63236638", "165595269", "433469962", "1134942774", "2971150995", "7778845732", "20364843314", "53316562617", "139583423242", "365436006810", "956720876191", "2504732642460" ]
[ "nonn", "easy" ]
92
0
1
[ "A000032", "A000045", "A001519", "A005522", "A006172", "A254884" ]
[ "M1915" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006172.seq
7d0f19b2d72e0b22d47afdeb20e5129e
A006173
Witt vector *2!.
[ "2", "1", "4", "13", "44", "135", "472", "1492", "5324", "17405", "63944", "215096", "799416", "2752909", "10310384", "36443256", "137263244", "489166324", "1860249448", "6739795717", "25596173800", "93596253769", "357974884304", "1319325363658", "5056389932088" ]
[ "nonn" ]
27
1
1
[ "A006173", "A006177", "A006973" ]
[ "M0174" ]
Simon Plouffe
2017-11-03T22:18:36
oeisdata/seq/A006/A006173.seq
e0b5bdef0003ffc6798640daf1339310
A006174
Witt vector *3!.
[ "6", "27", "488", "7974", "149796", "2725447", "56970432", "1151053821", "25279412332", "543871341927", "12411512060544", "278163517356594", "6498314231705568", "149846653983570795", "3565206002960088128", "84045618111578025105" ]
[ "nonn" ]
23
1
1
null
[ "M4180" ]
Simon Plouffe
2017-11-03T22:18:45
oeisdata/seq/A006/A006174.seq
cd16b928ae765d7638e4b6a2782f2797
A006175
Witt vector *4!.
[ "24", "972", "118592", "15210414", "2344956480", "377420590432", "67501965869568", "12329221295657241", "2383082885396731968", "467786496795764717088", "95188347941581635319296", "19578329367376510676884584" ]
[ "nonn" ]
22
1
1
null
[ "M5171" ]
Simon Plouffe
2017-11-03T22:18:53
oeisdata/seq/A006/A006175.seq
d14be8143dbefc88bf13f590504ac586
A006176
Witt vector *5!.
[ "120", "49500", "55480000", "75108093750", "124667171985024", "226899085942554400", "453922674315047424000", "954267187464733528198125", "2112236210012497151219800000", "4825706564405954731805322783552" ]
[ "nonn" ]
22
1
1
null
[ "M5383" ]
Simon Plouffe
2017-11-03T22:19:12
oeisdata/seq/A006/A006176.seq
44457d2509f94a6b4a15680346dcd78a
A006177
Witt vector *2!/2!.
[ "1", "1", "3", "8", "25", "72", "245", "772", "2692", "8925", "32065", "109890", "400023", "1402723", "5165327", "18484746", "68635477", "248339122", "930138521", "3406231198", "12810761323", "47306348881", "178987624513", "665627041157", "2528210175630", "9456885664122" ]
[ "nonn" ]
22
1
3
[ "A006173", "A006177", "A006973" ]
[ "M2750" ]
Simon Plouffe
2017-11-03T22:19:02
oeisdata/seq/A006/A006177.seq
cce21eae8c8bbe35da826dbef79f56fd
A006178
Witt vector *3!/3!.
[ "1", "7", "93", "1419", "25225", "472037", "9501737", "196190781", "4219610242", "92198459515", "2068590840349", "46897782768404", "1083052539395723", "25199771186287195", "594383312662808405", "14098935496013599680", "337939791145403719897" ]
[ "nonn" ]
22
1
2
null
[ "M4451" ]
Simon Plouffe
2017-11-03T22:19:18
oeisdata/seq/A006/A006178.seq
f1160108dfcb4f35e3e29550bdb3cedf
A006179
Witt vector *4!/4!.
[ "1", "52", "5133", "655554", "97772875", "16019720210", "2812609211657", "518332479161091", "99318252448110232", "19600890528520952329", "3966181169996511862429", "818653886943854653597621", "171938262068874336023196923" ]
[ "nonn" ]
21
1
2
null
[ "M5306" ]
Simon Plouffe
2017-11-03T22:19:25
oeisdata/seq/A006/A006179.seq
bb42e101c70802ddc00b53bef85370ce
A006180
Witt vector *5!/5!.
[ "1", "472", "467133", "636430764", "1038934571875", "1903882757758426", "3782689379194538057", "7975541699963490241566", "17602442746255160006062232", "40278440105728693363331297293" ]
[ "nonn" ]
24
1
2
null
[ "M5454" ]
Simon Plouffe
2017-11-03T22:19:32
oeisdata/seq/A006/A006180.seq
98fbadbd8c52c79f293b781a828d0391
A006181
Maximal partial Steiner triple systems of order n.
[ "1", "1", "1", "2", "2", "4", "10", "47", "472" ]
[ "nonn", "more" ]
17
3
4
null
[ "M0338" ]
N. J. A. Sloane.
2017-11-03T22:19:39
oeisdata/seq/A006/A006181.seq
947cec9619770dde63e2fa5b980541c9
A006182
Deficiencies of partial Steiner triple systems of order n.
[ "1", "1", "1", "2", "2", "4", "9", "22", "85" ]
[ "nonn", "more" ]
16
3
4
null
[ "M0334" ]
N. J. A. Sloane.
2017-11-03T22:19:46
oeisdata/seq/A006/A006182.seq
561502c45921b35114c162873fbe563c
A006183
a(n) = (n+1)*a(n-1) + (2-n)*a(n-2).
[ "1", "2", "6", "22", "98", "522", "3262", "23486", "191802", "1753618", "17755382", "197282022", "2387112466", "31249472282", "440096734638", "6635304614542", "106638824162282", "1819969265702946", "32873194861759462", "626524419718239158", "12565295306571352002", "264532532769923200042" ]
[ "nonn", "easy" ]
31
1
2
[ "A001339", "A006183", "A030297", "A054096" ]
[ "M1663" ]
N. J. A. Sloane, Simon Plouffe
2022-09-08T08:44:34
oeisdata/seq/A006/A006183.seq
1201362d7528a5480acf737af2c0bc0a
A006184
Number of cycles in the complement of a path.
[ "0", "0", "0", "0", "0", "3", "23", "153", "1077", "8490", "75234", "742710", "8084990", "96192405", "1241588865", "17277139383", "257810397243", "4106342523108", "69531388662932", "1247182219179900", "23622547999002444", "471129863595453495", "9868783491120925755", "216617163296681315685", "4971829898824570284305", "119096935551493905531438", "2972224576868227286710038", "77153543251103295197353938" ]
[ "nonn" ]
29
0
6
[ "A006184", "A302734" ]
[ "M3100" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A006/A006184.seq
1cc1087bde8f00cd22b9831f595c5358
A006185
Number of pair-coverings with largest block size 3.
[ "1", "4", "6", "7", "7", "12", "12", "19", "21", "26", "26", "35", "35", "46", "48", "57", "57", "70", "70", "85", "87", "100", "100", "117", "117", "136", "138", "155", "155", "176", "176", "199", "201", "222", "222", "247", "247", "274", "276", "301", "301", "330", "330", "361", "363", "392", "392", "425", "425", "460", "462", "495", "495", "532" ]
[ "nonn", "easy" ]
24
3
2
null
[ "M3266" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006185.seq
50e178abb69f6db96398741175e026e6
A006186
Number of pair-coverings with largest block size 4.
[ "1", "5", "8", "10", "11", "12", "12", "13", "13", "13" ]
[ "nonn", "hard", "more" ]
32
4
2
null
[ "M3773" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A006/A006186.seq
2b5165f55d7af13bb326a9a792ad0137
A006187
Number of pair-coverings with largest block size 5.
[ "1", "6", "10", "13", "15", "16", "16", "18" ]
[ "nonn" ]
10
5
2
null
[ "M4081" ]
N. J. A. Sloane.
2017-11-05T11:48:04
oeisdata/seq/A006/A006187.seq
7e114925b75f6d35474d110aefc53ad3
A006188
Maximal cycles in trivalent graphs.
[ "7", "15", "29", "57", "109", "213" ]
[ "nonn" ]
9
3
1
null
[ "M4350" ]
N. J. A. Sloane.
2017-11-05T11:48:30
oeisdata/seq/A006/A006188.seq
15f351e78a314afce6c20f784592a460
A006189
Number of self-avoiding walks of any length from NW to SW corners of a grid or lattice with n rows and 3 columns.
[ "1", "1", "3", "11", "38", "126", "415", "1369", "4521", "14933", "49322", "162900", "538021", "1776961", "5868903", "19383671", "64019918", "211443426", "698350195", "2306494009", "7617832221", "25159990673", "83097804242", "274453403400", "906458014441", "2993827446721", "9887940354603", "32657648510531" ]
[ "nonn", "walk", "easy" ]
70
0
3
[ "A001333", "A005409", "A006189", "A214931", "A216211", "A271465" ]
[ "M2891" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006189.seq
b0befecd966a69c9a774f12ab219882d
A006190
a(n) = 3*a(n-1) + a(n-2), with a(0)=0, a(1)=1.
[ "0", "1", "3", "10", "33", "109", "360", "1189", "3927", "12970", "42837", "141481", "467280", "1543321", "5097243", "16835050", "55602393", "183642229", "606529080", "2003229469", "6616217487", "21851881930", "72171863277", "238367471761", "787274278560", "2600190307441" ]
[ "nonn", "easy", "nice", "changed" ]
334
0
3
[ "A000045", "A000129", "A001076", "A005668", "A006190", "A006497", "A041025", "A041041", "A041061", "A041085", "A041113", "A041145", "A041181", "A049666", "A052906", "A052918", "A054413", "A054456", "A059317", "A092936", "A099371", "A140455", "A154597", "A175182", "A178765", "A201001", "A243399" ]
[ "M2844" ]
N. J. A. Sloane
2025-04-18T13:01:24
oeisdata/seq/A006/A006190.seq
d7888a472ca381fe372e141a37cd1061
A006191
Number of paths on square lattice.
[ "1", "2", "5", "16", "54", "180", "595", "1964", "6485", "21418", "70740", "233640", "771661", "2548622", "8417525", "27801196", "91821114", "303264540", "1001614735", "3308108744", "10925940965", "36085931638", "119183735880", "393637139280", "1300095153721", "4293922600442" ]
[ "nonn", "walk", "easy" ]
30
1
2
null
[ "M1490" ]
N. J. A. Sloane
2021-03-21T17:28:11
oeisdata/seq/A006/A006191.seq
01e1a51121e252a4a0b96d6e7739674c
A006192
Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of 3 X n board.
[ "1", "4", "12", "38", "125", "414", "1369", "4522", "14934", "49322", "162899", "538020", "1776961", "5868904", "19383672", "64019918", "211443425", "698350194", "2306494009", "7617832222", "25159990674", "83097804242", "274453403399", "906458014440" ]
[ "nonn", "walk", "nice", "easy" ]
45
1
2
[ "A006192", "A007764", "A007786", "A007787", "A064297", "A064298" ]
[ "M3453" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A006/A006192.seq
9195834ce4e07f0bd0bf329ccd4fd7ca
A006193
Number of n-node animals on cubic lattice.
[ "0", "1", "7", "58", "519", "4856", "46780", "460027", "4593647", "46416730", "473464492", "4866762231", "50346419064", "523649493732", "5471647249551", "57402510799673" ]
[ "nonn", "more" ]
24
0
3
null
[ "M4437" ]
Simon Plouffe
2018-02-18T20:32:42
oeisdata/seq/A006/A006193.seq
c7a48b69f8641ce030683b949ab0bda8
A006194
Number of n-node animals on f.c.c. lattice (invert A007199).
[ "1", "4", "19", "98", "531", "2971", "16997", "98830", "581788", "3458249", "20718292", "124929233", "757421601", "4613459330", "28213402944", "173141766742", "1065820341078" ]
[ "nonn" ]
23
1
2
null
[ "M3555" ]
Simon Plouffe and N. J. A. Sloane
2018-02-18T20:32:06
oeisdata/seq/A006/A006194.seq
29eaa2895dd382ea974e1248b60fb9bf
A006195
Reversion of Jacobi theta_3.
[ "1", "-2", "8", "-40", "222", "-1316", "8160", "-52272", "343220", "-2297682", "15623760", "-107611608", "749209832", "-5264005060", "37277153920", "-265788870480", "1906489923022", "-13747860118724", "99606357848920", "-724732875917064", "5293303253527704", "-38795196044205056" ]
[ "sign" ]
30
0
2
[ "A000122", "A006195", "A109085", "A181315" ]
null
N. J. A. Sloane
2023-09-27T02:45:13
oeisdata/seq/A006/A006195.seq
400b11d15212ebf3d8d85ca13055a33a
A006196
Number of leftist trees with n leaves.
[ "0", "1", "1", "1", "2", "4", "8", "17", "38", "87", "203", "482", "1160", "2822", "6929", "17149", "42736", "107144", "270060", "683940", "1739511", "4441255", "11378814", "29245927", "75386341", "194838673", "504802508", "1310843123", "3411070837", "8893590439", "23230151744", "60780377599", "159281030250" ]
[ "nonn", "nice" ]
74
0
5
[ "A006196", "A247448", "A247449" ]
[ "M1143" ]
N. J. A. Sloane
2025-01-10T12:38:39
oeisdata/seq/A006/A006196.seq
c9cb8ad1799041ce1d6d05fe61c20798
A006197
Least number not dividing binomial(2n,n).
[ "3", "4", "3", "3", "5", "5", "5", "4", "3", "3", "5", "3", "3", "7", "7", "4", "7", "8", "9", "8", "7", "7", "7", "7", "5", "5", "3", "3", "9", "3", "3", "4", "8", "8", "5", "3", "3", "9", "3", "3", "13", "13", "13", "11", "11", "11", "11", "8", "7", "5", "5", "5", "13", "9", "5", "5", "5", "7", "7", "5", "5", "5", "7", "4", "7", "7", "9", "8", "13", "7", "7" ]
[ "nonn" ]
19
1
1
[ "A000984", "A006197", "A007978", "A246655" ]
[ "M2297" ]
N. J. A. Sloane
2024-05-27T02:27:03
oeisdata/seq/A006/A006197.seq
54b5f234178302d8e6aef7bcd2158a40
A006198
Number of partitions into pairs.
[ "1", "1", "6", "41", "365", "3984", "51499", "769159", "13031514", "246925295", "5173842311", "118776068256", "2964697094281", "79937923931761", "2315462770608870", "71705109685449689", "2364107330976587909", "82676528225908987824", "3056806370495613000259", "119137361202296994159415" ]
[ "nonn" ]
52
1
3
null
[ "M4241" ]
N. J. A. Sloane
2018-11-14T14:07:48
oeisdata/seq/A006/A006198.seq
9eb39cbcb129378ebcd02e3d2615256a
A006199
Bessel polynomial {y_n}'(-1).
[ "0", "1", "-3", "21", "-185", "2010", "-25914", "386407", "-6539679", "123823305", "-2593076255", "59505341676", "-1484818160748", "40025880386401", "-1159156815431055", "35891098374564105", "-1183172853341759129", "41372997479943753582", "-1529550505546305534414", "59608871544962952539335" ]
[ "sign" ]
32
1
3
[ "A000806", "A001514", "A006199", "A065707", "A065920", "A065921", "A065922" ]
[ "M3082" ]
N. J. A. Sloane
2017-08-18T09:40:03
oeisdata/seq/A006/A006199.seq
d7f429da4b6225add66fc13347296cfc
A006200
Number of partitions into pairs.
[ "1", "6", "55", "610", "7980", "120274", "2052309", "39110490", "823324755", "18974858540", "475182478056", "12848667150956", "373081590628565", "11578264139795430", "382452947343624515", "13397354334102974934", "496082324933446766724", "19360538560004548357830", "794275868644522931369185" ]
[ "nonn" ]
21
1
2
[ "A006200", "A079267" ]
[ "M4263" ]
N. J. A. Sloane
2018-09-25T21:12:01
oeisdata/seq/A006/A006200.seq
aae2f2b123731eb838a3ce02ac573a43