christopher/oeis · Datasets at Hugging Face

a-number stringlengths 7 7	sequence sequencelengths 1 377	description stringlengths 3 852
A001201	[ "1", "1", "30", "840", "1197504000", "60281712691200", "1348410350618155344199680000" ]	Number of Steiner triple systems (STS's) on 6n+1 or 6n+3 elements.
A001202	[ "0", "1", "10", "2", "100", "11", "20", "3", "1000", "101", "110", "12", "200", "21", "30", "4", "10000", "1001", "1010", "102", "1100", "111", "120", "13", "2000", "201", "210", "22", "300", "31", "40", "5", "100000", "10001", "10010", "1002", "10100", "1011", "1020", "103", "11000", "1101", "1110", "112", "1200", "121", "130", "14", "20000", "2001", "2010" ]	a(1)=0, a(2n) = a(n)+1, a(2n+1) = 10*a(n+1).
A001203	[ "3", "7", "15", "1", "292", "1", "1", "1", "2", "1", "3", "1", "14", "2", "1", "1", "2", "2", "2", "2", "1", "84", "2", "1", "1", "15", "3", "13", "1", "4", "2", "6", "6", "99", "1", "2", "2", "6", "3", "5", "1", "1", "6", "8", "1", "7", "1", "2", "3", "7", "1", "2", "1", "1", "12", "1", "1", "1", "3", "1", "1", "8", "1", "1", "2", "1", "6", "1", "1", "5", "2", "2", "3", "1", "2", "4", "4", "16", "1", "161", "45", "1", "22", "1", "2", "2", "1", "4", "1", "2", "24", "1", "2", "1", "3", "1", "2", "1" ]	Simple continued fraction expansion of Pi.
A001204	[ "7", "2", "1", "1", "3", "18", "5", "1", "1", "6", "30", "8", "1", "1", "9", "42", "11", "1", "1", "12", "54", "14", "1", "1", "15", "66", "17", "1", "1", "18", "78", "20", "1", "1", "21", "90", "23", "1", "1", "24", "102", "26", "1", "1", "27", "114", "29", "1", "1", "30", "126", "32", "1", "1", "33", "138", "35", "1", "1", "36", "150", "38", "1", "1", "39", "162", "41", "1", "1", "42", "174", "44", "1", "1", "45", "186", "47", "1", "1" ]	Continued fraction for e^2.
A001205	[ "1", "0", "0", "1", "3", "12", "70", "465", "3507", "30016", "286884", "3026655", "34944085", "438263364", "5933502822", "86248951243", "1339751921865", "22148051088480", "388246725873208", "7193423109763089", "140462355821628771", "2883013994348484940" ]	Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.
A001206	[ "0", "1", "2", "4", "12", "81", "2646", "1422564", "229809982112", "423295099074735261880" ]	Number of self-dual monotone Boolean functions of n variables.
A001207	[ "1", "3", "11", "44", "186", "814", "3652", "16689", "77359", "362671", "1716033", "8182213", "39267086", "189492795", "918837374", "4474080844", "21866153748", "107217298977", "527266673134", "2599804551168", "12849503756579", "63646233127758", "315876691291677", "1570540515980274", "7821755377244303", "39014584984477092", "194880246951838595", "974725768600891269", "4881251640514912341", "24472502362094874818", "122826412768568196148", "617080993446201431307", "3103152024451536273288", "15618892303340118758816", "78679501136505611375745" ]	Number of fixed hexagonal polyominoes with n cells.
A001208	[ "3", "8", "15", "26", "35", "52", "69", "89", "112", "146", "172", "212", "259", "302", "354", "418", "476", "548", "633", "714", "805", "902", "1012", "1127", "1254", "1382", "1524", "1678", "1841", "2010", "2188", "2382", "2584", "2801", "3020", "3256", "3508", "3772", "4043", "4326", "4628", "4941", "5272", "5606", "5960", "6334", "6723", "7120" ]	a(n) = solution to the postage stamp problem with 3 denominations and n stamps.
A001209	[ "4", "12", "24", "44", "71", "114", "165", "234", "326", "427", "547", "708", "873", "1094", "1383", "1650", "1935", "2304", "2782", "3324", "3812", "4368", "5130", "5892", "6745", "7880", "8913", "9919", "11081", "12376", "13932", "15657", "17242", "18892", "21061", "23445", "25553", "27978", "31347", "33981", "36806", "39914", "43592" ]	a(n) is the solution to the postage stamp problem with 4 denominations and n stamps.
A001210	[ "5", "16", "36", "70", "126", "216", "345", "512", "797", "1055", "1475", "2047", "2659", "3403", "4422", "5629", "6865", "8669", "10835", "12903", "15785", "18801", "22456", "26469", "31108", "36949", "42744", "49436", "57033", "66771", "75558", "86303", "96852", "110253", "123954", "140688", "158389", "178811", "197293", "223580" ]	a(n) is the solution to the postage stamp problem with 5 denominations and n stamps.
A001211	[ "6", "20", "52", "108", "211", "388", "664", "1045", "1617", "2510", "3607", "5118", "7066", "9748", "12793", "17061", "22342", "28874", "36560", "45745", "57814", "72997", "87555", "106888", "129783" ]	a(n) is the solution to the postage stamp problem with 6 denominations and n stamps.
A001212	[ "2", "4", "8", "12", "16", "20", "26", "32", "40", "46", "54", "64", "72", "80", "92", "104", "116", "128", "140", "152", "164", "180", "196", "212" ]	a(n) = solution to the postage stamp problem with n denominations and 2 stamps.
A001213	[ "3", "7", "15", "24", "36", "52", "70", "93", "121", "154", "186", "225", "271", "323", "385", "450", "515", "606", "684", "788", "865", "977", "1091", "1201", "1361" ]	a(n) is the solution to the postage stamp problem with n denominations and 3 stamps.
A001214	[ "4", "10", "26", "44", "70", "108", "162", "228", "310", "422", "550", "700", "878", "1079", "1344", "1606", "1944", "2337", "2766", "3195", "3668", "4251", "4923", "5631", "6429" ]	a(n) is the solution to the postage stamp problem with n denominations and 4 stamps.
A001215	[ "5", "14", "35", "71", "126", "211", "336", "524", "726", "1016", "1393", "1871", "2494", "3196", "4063", "5113", "6511", "7949", "9865", "11589" ]	a(n) is the solution to the postage stamp problem with n denominations and 5 stamps.
A001216	[ "6", "18", "52", "114", "216", "388", "638", "1007", "1545", "2287" ]	a(n) = solution to the postage stamp problem with n denominations and 6 stamps.
A001217	[ "1", "2", "4", "6", "8", "12", "24", "48", "120", "192", "384", "720", "1152", "1920", "3840", "5040", "23040", "40320", "46080", "51840", "322560", "362880", "645120", "2903040", "3628800", "5160960", "10321920", "39916800", "92897280", "185794560", "479001600", "696729600", "1857945600", "3715891200" ]	Sorted list of orders of Weyl groups of types A_n, B_n, D_n, E_n, F_4, G_2.
A001218	[ "1", "3", "9", "27", "81", "43", "29", "87", "61", "83", "49", "47", "41", "23", "69", "7", "21", "63", "89", "67", "1", "3", "9", "27", "81", "43", "29", "87", "61", "83", "49", "47", "41", "23", "69", "7", "21", "63", "89", "67", "1", "3", "9", "27", "81", "43", "29", "87", "61", "83", "49", "47", "41", "23", "69", "7", "21", "63", "89", "67" ]	a(n) = 3^n mod 100.
A001219	[ "0", "6", "120", "210", "990", "185136", "258474216" ]	Triangular numbers of form a(a+1)(a+2).
A001220	[ "1093", "3511" ]	Wieferich primes: primes p such that p^2 divides 2^(p-1) - 1.
A001221	[ "0", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "1", "2", "2", "2", "2", "1", "2", "2", "2", "1", "3", "1", "2", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "2", "1", "3", "1", "2", "2", "1", "2", "3", "1", "2", "2", "3", "1", "2", "1", "2", "2", "2", "2", "3", "1", "2", "1", "2", "1", "3", "2", "2", "2", "2", "1", "3", "2", "2", "2", "2", "2", "2", "1", "2", "2", "2", "1", "3", "1", "2", "3", "2", "1", "2", "1", "3", "2" ]	Number of distinct primes dividing n (also called omega(n)).
A001222	[ "0", "1", "1", "2", "1", "2", "1", "3", "2", "2", "1", "3", "1", "2", "2", "4", "1", "3", "1", "3", "2", "2", "1", "4", "2", "2", "3", "3", "1", "3", "1", "5", "2", "2", "2", "4", "1", "2", "2", "4", "1", "3", "1", "3", "3", "2", "1", "5", "2", "3", "2", "3", "1", "4", "2", "4", "2", "2", "1", "4", "1", "2", "3", "6", "2", "3", "1", "3", "2", "3", "1", "5", "1", "2", "3", "3", "2", "3", "1", "5", "4", "2", "1", "4", "2", "2", "2", "4", "1", "4", "2", "3", "2", "2", "2", "6", "1", "3", "3", "4", "1", "3", "1", "4", "3", "2", "1", "5", "1", "3", "2" ]	Number of prime divisors of n counted with multiplicity (also called big omega of n, bigomega(n) or Omega(n)).
A001223	[ "1", "2", "2", "4", "2", "4", "2", "4", "6", "2", "6", "4", "2", "4", "6", "6", "2", "6", "4", "2", "6", "4", "6", "8", "4", "2", "4", "2", "4", "14", "4", "6", "2", "10", "2", "6", "6", "4", "6", "6", "2", "10", "2", "4", "2", "12", "12", "4", "2", "4", "6", "2", "10", "6", "6", "6", "2", "6", "4", "2", "10", "14", "4", "2", "4", "14", "6", "10", "2", "4", "6", "8", "6", "6", "4", "6", "8", "4", "8", "10", "2", "10", "2", "6", "4", "6", "8", "4", "2", "4", "12", "8", "4", "8", "4", "6", "12" ]	Prime gaps: differences between consecutive primes.
A001224	[ "1", "2", "2", "4", "5", "9", "12", "21", "30", "51", "76", "127", "195", "322", "504", "826", "1309", "2135", "3410", "5545", "8900", "14445", "23256", "37701", "60813", "98514", "159094", "257608", "416325", "673933", "1089648", "1763581", "2852242", "4615823", "7466468", "12082291", "19546175", "31628466" ]	If F(n) is the n-th Fibonacci number, then a(2n) = (F(2n+1) + F(n+2))/2 and a(2n+1) = (F(2n+2) + F(n+1))/2.
A001225	[ "1", "2", "5", "7", "11", "14", "20", "24", "30", "35", "44", "50" ]	Number of consistent arcs in a tournament with n nodes.
A001226	[ "1", "1", "3", "9", "7", "93", "315", "17", "3855", "13797", "195", "182361", "41943", "9709", "9256395", "34636833", "31775", "479349", "1857283155", "430185", "26817356775", "102280151421", "372827", "1497207322929", "89756051247", "84215045", "84973577874915", "19991120505", "1205604855", "4885260612740877" ]	Lerch's function q_2(n) = (2^{phi(t)} - 1)/t where t = 2*n - 1.
A001227	[ "1", "1", "2", "1", "2", "2", "2", "1", "3", "2", "2", "2", "2", "2", "4", "1", "2", "3", "2", "2", "4", "2", "2", "2", "3", "2", "4", "2", "2", "4", "2", "1", "4", "2", "4", "3", "2", "2", "4", "2", "2", "4", "2", "2", "6", "2", "2", "2", "3", "3", "4", "2", "2", "4", "4", "2", "4", "2", "2", "4", "2", "2", "6", "1", "4", "4", "2", "2", "4", "4", "2", "3", "2", "2", "6", "2", "4", "4", "2", "2", "5", "2", "2", "4", "4", "2", "4", "2", "2", "6", "4", "2", "4", "2", "4", "2", "2", "3", "6", "3", "2", "4", "2", "2", "8" ]	Number of odd divisors of n.
A001228	[ "7920", "95040", "175560", "443520", "604800", "10200960", "44352000", "50232960", "244823040", "898128000", "4030387200", "145926144000", "448345497600", "460815505920", "495766656000", "42305421312000", "64561751654400", "273030912000000", "51765179004000000", "90745943887872000", "4089470473293004800", "4157776806543360000", "86775571046077562880", "1255205709190661721292800", "4154781481226426191177580544000000", "808017424794512875886459904961710757005754368000000000" ]	Orders of sporadic simple groups.
A001229	[ "1", "2", "8", "12", "128", "240", "720", "6912", "32768", "142560", "712800", "1140480", "1190400", "3345408", "3571200", "5702400", "14859936", "29719872", "50319360", "118879488", "2147483648", "3889036800", "4389396480", "21946982400", "47416320000", "92177326080", "133145026560", "331914240000" ]	Numbers n such that phi(sigma(n)) = n.
A001230	[ "0", "0", "9862", "13267364410532" ]	Number of undirected closed knight's tours on a 2n X 2n chessboard.
A001231	[ "1", "1", "1", "1", "0", "1", "1", "4", "0" ]	Number of nonisomorphic projective planes of order n.
A001232	[ "1089", "10989", "109989", "1099989", "10891089", "10999989", "108901089", "109999989", "1089001089", "1098910989", "1099999989", "10890001089", "10989010989", "10999999989", "108900001089", "108910891089", "109890010989", "109989109989", "109999999989", "1089000001089", "1089109891089" ]	Numbers k such that 9*k = (k written backwards), k > 0.
A001233	[ "1", "21", "322", "4536", "63273", "902055", "13339535", "206070150", "3336118786", "56663366760", "1009672107080", "18861567058880", "369012649234384", "7551527592063024", "161429736530118960", "3599979517947607200", "83637381699544802976", "2021687376910682741568", "50779532534302850198976", "1323714091579185857760000" ]	Unsigned Stirling numbers of first kind s(n,6).
A001234	[ "1", "28", "546", "9450", "157773", "2637558", "44990231", "790943153", "14409322928", "272803210680", "5374523477960", "110228466184200", "2353125040549984", "52260903362512720", "1206647803780373360", "28939583397335447760" ]	Unsigned Stirling numbers of the first kind s(n,7).
A001235	[ "1729", "4104", "13832", "20683", "32832", "39312", "40033", "46683", "64232", "65728", "110656", "110808", "134379", "149389", "165464", "171288", "195841", "216027", "216125", "262656", "314496", "320264", "327763", "373464", "402597", "439101", "443889", "513000", "513856", "515375", "525824", "558441", "593047", "684019", "704977" ]	Taxi-cab numbers: sums of 2 cubes in more than 1 way.
A001236	[ "15", "575", "46760", "6998824", "1744835904", "673781602752", "381495483224064", "303443622431870976", "327643295527342080000", "466962174913357393920000", "858175477913267353681920000", "1993920215002599923346309120000", "5758788816015998806424467537920000" ]	Differences of reciprocals of unity.
A001237	[ "31", "3661", "1217776", "929081776", "1413470290176", "3878864920694016", "17810567950611972096", "129089983180418186674176", "1409795030885143760732160000", "22335321387514981111936450560000" ]	Differences of reciprocals of unity.
A001238	[ "63", "22631", "30480800", "117550462624", "1083688832185344", "21006340945438768128", "778101042571221893382144", "51150996584622542869024997376", "5626686079269855254796985958400000", "987233834003503822099304377378406400000" ]	Differences of reciprocals of unity.
A001239	[ "216", "251", "344", "729", "855", "1009", "1072", "1366", "1457", "1459", "1520", "1674", "1728", "1729", "1730", "1737", "1756", "1763", "1793", "1854", "1945", "2008", "2072", "2241", "2414", "2456", "2458", "2729", "2736", "2752", "3060", "3391", "3402", "3457", "3500", "3592", "3599", "3655", "3744", "3745" ]	Numbers that are the sum of 3 nonnegative cubes in more than 1 way.
A001240	[ "1", "11", "85", "575", "3661", "22631", "137845", "833375", "5019421", "30174551", "181222405", "1087861775", "6528756781", "39177307271", "235078159765", "1410511939775", "8463200647741", "50779591044791", "304678708005925" ]	Expansion of 1/((1-2x)(1-3x)(1-6x)).
A001241	[ "1", "50", "1660", "46760", "1217776", "30480800", "747497920", "18139003520", "437786795776", "10536798272000", "253246254177280", "6082300519393280", "146028165842661376", "3505313580591718400", "84135194495708938240", "2019336829962040279040" ]	Differences of reciprocals of unity.
A001242	[ "1", "274", "48076", "6998824", "929081776", "117550462624", "14500866102976", "1765130436471424", "213373597575314176", "25700650466807540224", "3089923562153380965376", "371145495540181143169024", "44558899569395347436056576", "5348360831598738338465357824" ]	Differences of reciprocals of unity.
A001243	[ "1", "247", "14608", "455192", "9738114", "162512286", "2275172004", "27971176092", "311387598411", "3207483178157", "31055652948388", "285997074307300", "2527925001876036", "21598596303099900", "179385804170146680" ]	Eulerian numbers (Euler's triangle: column k=7 of A008292, column k=6 of A173018).
A001244	[ "1", "502", "47840", "2203488", "66318474", "1505621508", "27971176092", "447538817472", "6382798925475", "83137223185370", "1006709967915228", "11485644635009424", "124748182104463860", "1300365805079109480", "13093713503185076040" ]	Eulerian numbers (Euler's triangle: column k=8 of A008292, column k=7 of A173018).
A001245	[ "81", "126", "128", "216", "217", "219", "224", "243", "251", "252", "259", "278", "280", "315", "341", "343", "344", "345", "352", "371", "376", "378", "405", "408", "432", "434", "467", "469", "496", "522", "540", "559", "560", "567", "584", "593", "594", "648", "687", "702", "728", "729", "730", "737", "756", "758", "763", "765", "783", "793", "802" ]	Numbers that are the sum of 4 cubes in more than 1 way.
A001246	[ "1", "1", "4", "25", "196", "1764", "17424", "184041", "2044900", "23639044", "282105616", "3455793796", "43268992144", "551900410000", "7152629313600", "93990019574025", "1250164827828900", "16807771574144100", "228138727737690000", "3123219182728976100", "43087676888260976400", "598598221893939680400", "8369059450146650049600" ]	Squares of Catalan numbers.
A001247	[ "1", "1", "4", "25", "225", "2704", "41209", "769129", "17139600", "447195609", "13450200625", "460457244900", "17754399678409", "764214897046969", "36442551140059684", "1912574337188517025", "109833379421325769609", "6866586647633870998416", "465228769500062060333281" ]	Squares of Bell numbers.
A001248	[ "4", "9", "25", "49", "121", "169", "289", "361", "529", "841", "961", "1369", "1681", "1849", "2209", "2809", "3481", "3721", "4489", "5041", "5329", "6241", "6889", "7921", "9409", "10201", "10609", "11449", "11881", "12769", "16129", "17161", "18769", "19321", "22201", "22801", "24649", "26569", "27889", "29929", "32041", "32761", "36481" ]	Squares of primes.
A001249	[ "1", "16", "100", "400", "1225", "3136", "7056", "14400", "27225", "48400", "81796", "132496", "207025", "313600", "462400", "665856", "938961", "1299600", "1768900", "2371600", "3136441", "4096576", "5290000", "6760000", "8555625", "10732176", "13351716", "16483600", "20205025", "24601600", "29767936", "35808256" ]	Squares of tetrahedral numbers: a(n) = binomial(n+3,n)^2.
A001250	[ "1", "1", "2", "4", "10", "32", "122", "544", "2770", "15872", "101042", "707584", "5405530", "44736512", "398721962", "3807514624", "38783024290", "419730685952", "4809759350882", "58177770225664", "740742376475050", "9902996106248192", "138697748786275802", "2030847773013704704", "31029068327114173810" ]	Number of alternating permutations of order n.
A001251	[ "0", "0", "2", "12", "70", "442", "3108", "24216", "208586", "1972904", "20373338", "228346522", "2763212980", "35926266244", "499676669254", "7405014187564", "116511984902094", "1940073930857802", "34087525861589564", "630296344519286304", "12235215845125112122", "248789737587365945992" ]	Number of permutations of order n with the length of longest run equal 3.
A001252	[ "0", "0", "0", "2", "16", "134", "1164", "10982", "112354", "1245676", "14909340", "191916532", "2646100822", "38932850396", "609137502242", "10101955358506", "177053463254274", "3270694371428814", "63524155236581118", "1294248082658393546", "27604013493657933856", "615135860462018980316" ]	Number of permutations of order n with the length of longest run equal 4.
A001253	[ "0", "0", "0", "0", "2", "20", "198", "2048", "22468", "264538", "3340962", "45173518", "652209564", "10024669626", "163546399460", "2823941647390", "51468705947590", "987671243816650", "19909066390361346", "420650676776338140", "9297308938203169622", "214562999510569012168" ]	Number of permutations of order n with the length of longest run equal 5.
A001254	[ "4", "1", "9", "16", "49", "121", "324", "841", "2209", "5776", "15129", "39601", "103684", "271441", "710649", "1860496", "4870849", "12752041", "33385284", "87403801", "228826129", "599074576", "1568397609", "4106118241", "10749957124", "28143753121", "73681302249", "192900153616", "505019158609", "1322157322201", "3461452808004", "9062201101801", "23725150497409" ]	Squares of Lucas numbers.
A001255	[ "1", "1", "4", "9", "25", "49", "121", "225", "484", "900", "1764", "3136", "5929", "10201", "18225", "30976", "53361", "88209", "148225", "240100", "393129", "627264", "1004004", "1575025", "2480625", "3833764", "5934096", "9060100", "13823524", "20839225", "31404816", "46812964", "69705801", "102880449", "151536100" ]	Squares of partition numbers.
A001256	[ "1", "1", "1", "1", "4", "9", "36", "121", "529", "2209", "11236", "55225", "303601", "1692601", "9979281", "59923081", "373262400", "2364779641", "15343033689", "101095382025", "677435994225", "4598901695025", "31626631547536", "219871778549476", "1544481904210609", "10948878748872100", "78284374662902500" ]	Squares of numbers of trees.
A001257	[ "1", "1", "4", "16", "81", "400", "2304", "13225", "81796", "516961", "3392964", "22714756", "155900196", "1087218729", "7710771721", "55404215161", "403030713409", "2962388303281", "21983682632976", "164512124707984", "1240577449436224" ]	Squares of numbers of rooted trees.
A001258	[ "1", "1", "2", "6", "25", "135", "892", "6937", "61886", "621956", "6946471", "85302935", "1141820808", "16540534553", "257745010762", "4298050731298", "76356627952069", "1439506369337319", "28699241994332940", "603229325513240569", "13330768181611378558", "308967866671489907656", "7493481669479297191451", "189793402599733802743015", "5010686896406348299630712" ]	Number of labeled n-node trees with unlabeled end-points.
A001259	[ "3", "5", "7", "17", "19", "37", "97", "113", "257", "401", "487", "631", "971", "1297", "1801", "19457", "22051", "28817", "65537", "157303", "160001" ]	A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1p_2...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.
A001260	[ "0", "0", "0", "0", "1", "5", "45", "385", "3710", "38934", "444990", "5506710", "73422855", "1049946755", "16035550531", "260577696015", "4489954146860", "81781307674780", "1570201107355980", "31698434854748604", "671260973394676605", "14879618243581997745" ]	Number of permutations of length n with 4 consecutive ascending pairs.
A001261	[ "0", "0", "0", "0", "0", "1", "6", "63", "616", "6678", "77868", "978978", "13216104", "190899423", "2939850914", "48106651593", "833848627248", "15265844099324", "294412707629208", "5966764207952724", "126793739418994416", "2819296088257641741", "65470320271760790078" ]	Number of permutations of length n with 5 consecutive ascending pairs.
A001262	[ "2047", "3277", "4033", "4681", "8321", "15841", "29341", "42799", "49141", "52633", "65281", "74665", "80581", "85489", "88357", "90751", "104653", "130561", "196093", "220729", "233017", "252601", "253241", "256999", "271951", "280601", "314821", "357761", "390937", "458989", "476971", "486737" ]	Strong pseudoprimes to base 2.
A001263	[ "1", "1", "1", "1", "3", "1", "1", "6", "6", "1", "1", "10", "20", "10", "1", "1", "15", "50", "50", "15", "1", "1", "21", "105", "175", "105", "21", "1", "1", "28", "196", "490", "490", "196", "28", "1", "1", "36", "336", "1176", "1764", "1176", "336", "36", "1", "1", "45", "540", "2520", "5292", "5292", "2520", "540", "45", "1", "1", "55", "825", "4950", "13860", "19404", "13860", "4950", "825" ]	Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.
A001264	[ "1", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96" ]	Final 2 digits of 4^n.
A001265	[ "0", "1", "3", "7", "3", "5", "31", "3", "3", "7", "127", "3", "5", "17", "7", "73", "3", "11", "31", "23", "89", "3", "3", "5", "7", "13", "8191", "3", "43", "127", "7", "31", "151", "3", "5", "17", "257", "131071", "3", "3", "3", "7", "19", "73", "524287", "3", "5", "5", "11", "31", "41", "7", "7", "127", "337", "3", "23", "89", "683", "47", "178481", "3", "3", "5", "7", "13", "17", "241" ]	Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.
A001266	[ "0", "0", "1", "7", "45", "323", "2621", "23811", "239653", "2648395", "31889517", "415641779", "5830753109", "87601592187", "1403439027805", "23883728565283", "430284458893701", "8181419271349931", "163730286973255373", "3440164703027845395", "75718273707281368117", "1742211593431076483419" ]	One-half the number of permutations of length n without rising or falling successions.
A001267	[ "0", "0", "0", "0", "1", "8", "60", "444", "3599", "32484", "325322", "3582600", "43029621", "559774736", "7841128936", "117668021988", "1883347579515", "32026067455084", "576605574327174", "10957672400252944", "219190037987444577", "4603645435776504120", "101292568208941883236", "2329975164242735146316" ]	One-half the number of permutations of length n with exactly 3 rising or falling successions.
A001268	[ "0", "0", "0", "0", "0", "1", "11", "113", "1099", "11060", "118484", "1366134", "16970322", "226574211", "3240161105", "49453685911", "802790789101", "13815657556958", "251309386257874", "4818622686395380", "97145520138758844", "2054507019515346789", "45484006970415223287", "1052036480881734378541" ]	One-half the number of permutations of length n with exactly 4 rising or falling successions.
A001269	[ "2", "3", "5", "3", "3", "17", "3", "11", "5", "13", "3", "43", "257", "3", "3", "3", "19", "5", "5", "41", "3", "683", "17", "241", "3", "2731", "5", "29", "113", "3", "3", "11", "331", "65537", "3", "43691", "5", "13", "37", "109", "3", "174763", "17", "61681", "3", "3", "43", "5419", "5", "397", "2113", "3", "2796203", "97", "257", "673", "3", "11", "251", "4051" ]	Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), with repetition.
A001270	[ "3", "3", "3", "3", "11", "3", "3", "3", "37", "3", "3", "11", "101", "3", "3", "41", "271", "3", "3", "3", "7", "11", "13", "37", "3", "3", "239", "4649", "3", "3", "11", "73", "101", "137", "3", "3", "3", "3", "37", "333667", "3", "3", "11", "41", "271", "9091", "3", "3", "21649", "513239", "3", "3", "3", "7", "11", "13", "37", "101", "9901", "3", "3", "53", "79", "265371653" ]	Table of prime factors of 10^n - 1 (with multiplicity).
A001271	[ "2", "11", "101", "7", "11", "13", "73", "137", "11", "9091", "101", "9901", "11", "909091", "17", "5882353", "7", "11", "13", "19", "52579", "101", "3541", "27961", "11", "11", "23", "4093", "8779", "73", "137", "99990001", "11", "859", "1058313049", "29", "101", "281", "121499449", "7", "11", "13", "211", "241", "2161", "9091", "353", "449", "641", "1409", "69857" ]	Irregular table read by rows: row n lists prime factors of 10^n +1, with multiplicity.
A001272	[ "3", "4", "5", "6", "7", "8", "10", "15", "19", "41", "59", "61", "105", "160", "661", "2653", "3069", "3943", "4053", "4998", "8275", "9158", "11164", "43592", "59961" ]	Numbers k such that k! - (k-1)! + (k-2)! - (k-3)! + ... - (-1)^k*1! is prime.
A001273	[ "1", "10", "13", "23", "19", "7", "356", "78999" ]	Smallest number that takes n steps to reach 1 under iteration of sum-of-squares-of-digits map (= smallest "happy number" of height n).
A001274	[ "1", "3", "15", "104", "164", "194", "255", "495", "584", "975", "2204", "2625", "2834", "3255", "3705", "5186", "5187", "10604", "11715", "13365", "18315", "22935", "25545", "32864", "38804", "39524", "46215", "48704", "49215", "49335", "56864", "57584", "57645", "64004", "65535", "73124", "105524", "107864", "123824", "131144", "164175", "184635" ]	Numbers k such that phi(k) = phi(k+1).
A001275	[ "3", "7", "23", "61", "127", "199", "337", "479", "677", "937", "1193", "1511", "1871", "2267", "2707", "3251", "3769", "4349", "5009", "5711", "6451", "7321", "8231", "9173", "10151", "11197", "12343", "13487", "14779", "16097", "17599", "19087", "20563", "22109", "23761", "25469", "27259", "29123", "31081", "33029" ]	Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2.
A001276	[ "2", "3", "7", "15", "27", "41", "62", "85", "115", "150", "186", "229", "274", "323", "380", "443", "509", "577", "653", "733", "818", "912", "1010", "1114", "1222", "1331", "1448", "1572", "1704", "1845", "1994", "2138", "2289", "2445", "2609", "2774", "2948", "3127", "3311", "3502", "3699", "3900", "4112", "4324", "4546", "4775", "5016", "5255", "5493" ]	Smallest k such that the product of q/(q-1) over the primes from prime(n) to prime(n+k-1) is greater than 2.
A001277	[ "1", "3", "12", "56", "321", "2175", "17008", "150504", "1485465", "16170035", "192384876", "2483177808", "34554278857", "515620794591", "8212685046336", "139062777326000", "2494364438359953", "47245095998005059", "942259727190907180", "19737566982241851720", "433234326593362631601", "9943659797649140568863" ]	Number of permutations of length n by rises.
A001278	[ "1", "11", "87", "693", "5934", "55674", "572650", "6429470", "78366855", "1031378445", "14583751161", "220562730171", "3553474061452", "60765835154948", "1099353888345924", "20980355229808524", "421242574828254525", "8876636475162819615", "195887449298481357835", "4517865858233007694865", "108699311713253202373146", "2723633081926998772488606" ]	Number of permutations of length n by rises.
A001279	[ "3", "53", "680", "8064", "96370", "1200070", "15778800", "220047400", "3257228485", "51125192475", "849388162448", "14905775547488", "275697902983860", "5362979000259804", "109488815508733440", "2341353038132316240", "52346701837709016375", "1221458048752142672625", "29697803502485749344120", "751211166036942984639200" ]	Number of permutations of length n by rises.
A001280	[ "11", "309", "5805", "95575", "1516785", "24206055", "396475975", "6733084365", "119143997490", "2201649739310", "42514526708766", "857750898213594", "18068801884373310", "397038791150060850", "9090755207499817170", "216635190303090215910" ]	Number of permutations of length n by rises.
A001281	[ "0", "2", "1", "8", "2", "14", "3", "20", "4", "26", "5", "32", "6", "38", "7", "44", "8", "50", "9", "56", "10", "62", "11", "68", "12", "74", "13", "80", "14", "86", "15", "92", "16", "98", "17", "104", "18", "110", "19", "116", "20", "122", "21", "128", "22", "134", "23", "140", "24", "146", "25", "152", "26", "158", "27", "164", "28", "170", "29", "176", "30", "182", "31", "188" ]	Image of n under the map n->n/2 if n even, n->3n-1 if n odd.
A001282	[ "17", "259", "2770", "27978", "294602", "3331790", "40682144", "535206440", "7557750635", "114101726625", "1834757172082", "31313852523634", "565434670633580", "10771030900532868", "215881317066455232", "4541623615098815280" ]	Number of permutations of length n by rises.
A001283	[ "6", "12", "15", "20", "24", "28", "30", "35", "40", "45", "42", "48", "54", "60", "66", "56", "63", "70", "77", "84", "91", "72", "80", "88", "96", "104", "112", "120", "90", "99", "108", "117", "126", "135", "144", "153", "110", "120", "130", "140", "150", "160", "170", "180", "190", "132", "143", "154", "165", "176", "187", "198", "209", "220", "231", "156", "168", "180" ]	Triangle read by rows, in which row n consists of n(n+m) for m = 1 .. n-1.
A001284	[ "6", "12", "15", "20", "24", "28", "30", "35", "40", "42", "45", "48", "54", "56", "60", "63", "66", "70", "72", "77", "80", "84", "88", "90", "91", "96", "99", "104", "108", "110", "112", "117", "120", "126", "130", "132", "135", "140", "143", "144", "150", "153", "154", "156", "160", "165", "168", "170", "176", "180", "182", "187", "190", "192", "195", "198", "204", "208", "209", "210", "216", "220", "221", "224", "228", "231" ]	Numbers of form m*k with m+1 <= k <= 2m-1.
A001285	[ "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1" ]	Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 1's and 2's.
A001286	[ "1", "6", "36", "240", "1800", "15120", "141120", "1451520", "16329600", "199584000", "2634508800", "37362124800", "566658892800", "9153720576000", "156920924160000", "2845499424768000", "54420176498688000", "1094805903679488000", "23112569077678080000" ]	Lah numbers: a(n) = (n-1)*n!/2.
A001287	[ "1", "11", "66", "286", "1001", "3003", "8008", "19448", "43758", "92378", "184756", "352716", "646646", "1144066", "1961256", "3268760", "5311735", "8436285", "13123110", "20030010", "30045015", "44352165", "64512240", "92561040", "131128140", "183579396", "254186856", "348330136", "472733756", "635745396" ]	a(n) = binomial coefficient C(n,10).
A001288	[ "1", "12", "78", "364", "1365", "4368", "12376", "31824", "75582", "167960", "352716", "705432", "1352078", "2496144", "4457400", "7726160", "13037895", "21474180", "34597290", "54627300", "84672315", "129024480", "193536720", "286097760", "417225900", "600805296", "854992152", "1203322288", "1676056044" ]	a(n) = binomial(n,11).
A001289	[ "1", "2", "3", "8", "48", "150357", "63379147320777408548" ]	Number of equivalence classes of Boolean functions modulo linear functions.
A001290	[ "192", "21504", "10321924" ]	Order of "Restricted Affine Group" on n variables.
A001291	[ "13", "28", "62", "124" ]	Number of conjugacy classes in Restricted Affine Group on n variables.
A001292	[ "1", "12", "21", "123", "231", "312", "1234", "2341", "3412", "4123", "12345", "23451", "34512", "45123", "51234", "123456", "234561", "345612", "456123", "561234", "612345", "1234567", "2345671", "3456712", "4567123", "5671234", "6712345", "7123456" ]	Concatenations of cyclic permutations of initial positive integers.
A001293	[ "759", "506", "253", "330", "176", "77", "210", "120", "56", "21", "130", "80", "40", "16", "5", "78", "52", "28", "12", "4", "1", "46", "32", "20", "8", "4", "0", "1", "30", "16", "16", "4", "4", "0", "0", "1", "30", "0", "16", "0", "4", "0", "0", "0", "1" ]	Leech triangle: k-th number (0 <= k <= n) in n-th row (0 <= n) is number of octads in S(5,8,24) containing k given points and missing n-k given points.
A001294	[ "2576", "1288", "1288", "616", "672", "616", "280", "336", "336", "280", "120", "160", "176", "160", "120", "48", "72", "88", "88", "72", "48", "16", "32", "40", "48", "40", "32", "16", "0", "16", "16", "24", "24", "16", "16", "0", "0", "0", "16", "0", "24", "0", "16", "0", "0" ]	Triangle in which k-th number (0<=k<=n) in n-th row (0<=n) is number of dodecads in Golay code G_24 containing k given points and missing n-k given points.
A001295	[ "132", "66", "66", "30", "36", "30", "12", "18", "18", "12", "4", "8", "10", "8", "4", "1", "3", "5", "5", "3", "1", "1", "0", "3", "2", "3", "0", "1" ]	Triangle in which k-th number (0<=k<=n) in n-th row (0<=n) is number of hexads in S(5,6,12) containing k given points and missing n-k given points.
A001296	[ "0", "1", "7", "25", "65", "140", "266", "462", "750", "1155", "1705", "2431", "3367", "4550", "6020", "7820", "9996", "12597", "15675", "19285", "23485", "28336", "33902", "40250", "47450", "55575", "64701", "74907", "86275", "98890", "112840", "128216", "145112", "163625", "183855", "205905", "229881", "255892", "284050", "314470" ]	4-dimensional pyramidal numbers: a(n) = (3n+1)binomial(n+2, 3)/4. Also Stirling2(n+2, n).
A001297	[ "0", "1", "15", "90", "350", "1050", "2646", "5880", "11880", "22275", "39325", "66066", "106470", "165620", "249900", "367200", "527136", "741285", "1023435", "1389850", "1859550", "2454606", "3200450", "4126200", "5265000", "6654375", "8336601", "10359090", "12774790", "15642600", "19027800" ]	Stirling numbers of the second kind S(n+3, n).
A001298	[ "0", "1", "31", "301", "1701", "6951", "22827", "63987", "159027", "359502", "752752", "1479478", "2757118", "4910178", "8408778", "13916778", "22350954", "34952799", "53374629", "79781779", "116972779", "168519505", "238929405", "333832005", "460192005", "626551380", "843303006", "1122998436", "1480692556" ]	Stirling numbers of the second kind S(n+4, n).
A001299	[ "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "4", "4", "4", "4", "4", "6", "6", "6", "6", "6", "9", "9", "9", "9", "9", "13", "13", "13", "13", "13", "18", "18", "18", "18", "18", "24", "24", "24", "24", "24", "31", "31", "31", "31", "31", "39", "39", "39", "39", "39", "49", "49", "49", "49", "49", "60", "60", "60", "60", "60", "73", "73", "73", "73", "73", "87", "87", "87", "87", "87", "103", "103", "103", "103", "103" ]	Number of ways of making change for n cents using coins of 1, 5, 10, 25 cents.
A001300	[ "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "4", "4", "4", "4", "4", "6", "6", "6", "6", "6", "9", "9", "9", "9", "9", "13", "13", "13", "13", "13", "18", "18", "18", "18", "18", "24", "24", "24", "24", "24", "31", "31", "31", "31", "31", "39", "39", "39", "39", "39", "50", "50", "50", "50", "50", "62", "62", "62", "62", "62", "77", "77", "77" ]	Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 cents.

A001201

[ "1", "1", "30", "840", "1197504000", "60281712691200", "1348410350618155344199680000" ]

Number of Steiner triple systems (STS's) on 6n+1 or 6n+3 elements.

A001202

[ "0", "1", "10", "2", "100", "11", "20", "3", "1000", "101", "110", "12", "200", "21", "30", "4", "10000", "1001", "1010", "102", "1100", "111", "120", "13", "2000", "201", "210", "22", "300", "31", "40", "5", "100000", "10001", "10010", "1002", "10100", "1011", "1020", "103", "11000", "1101", "1110", "112", "1200", "121", "130", "14", "20000", "2001", "2010" ]

a(1)=0, a(2n) = a(n)+1, a(2n+1) = 10*a(n+1).

A001203

[ "3", "7", "15", "1", "292", "1", "1", "1", "2", "1", "3", "1", "14", "2", "1", "1", "2", "2", "2", "2", "1", "84", "2", "1", "1", "15", "3", "13", "1", "4", "2", "6", "6", "99", "1", "2", "2", "6", "3", "5", "1", "1", "6", "8", "1", "7", "1", "2", "3", "7", "1", "2", "1", "1", "12", "1", "1", "1", "3", "1", "1", "8", "1", "1", "2", "1", "6", "1", "1", "5", "2", "2", "3", "1", "2", "4", "4", "16", "1", "161", "45", "1", "22", "1", "2", "2", "1", "4", "1", "2", "24", "1", "2", "1", "3", "1", "2", "1" ]

Simple continued fraction expansion of Pi.

A001204

[ "7", "2", "1", "1", "3", "18", "5", "1", "1", "6", "30", "8", "1", "1", "9", "42", "11", "1", "1", "12", "54", "14", "1", "1", "15", "66", "17", "1", "1", "18", "78", "20", "1", "1", "21", "90", "23", "1", "1", "24", "102", "26", "1", "1", "27", "114", "29", "1", "1", "30", "126", "32", "1", "1", "33", "138", "35", "1", "1", "36", "150", "38", "1", "1", "39", "162", "41", "1", "1", "42", "174", "44", "1", "1", "45", "186", "47", "1", "1" ]

Continued fraction for e^2.

A001205

[ "1", "0", "0", "1", "3", "12", "70", "465", "3507", "30016", "286884", "3026655", "34944085", "438263364", "5933502822", "86248951243", "1339751921865", "22148051088480", "388246725873208", "7193423109763089", "140462355821628771", "2883013994348484940" ]

Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.

A001206

[ "0", "1", "2", "4", "12", "81", "2646", "1422564", "229809982112", "423295099074735261880" ]

Number of self-dual monotone Boolean functions of n variables.

A001207

[ "1", "3", "11", "44", "186", "814", "3652", "16689", "77359", "362671", "1716033", "8182213", "39267086", "189492795", "918837374", "4474080844", "21866153748", "107217298977", "527266673134", "2599804551168", "12849503756579", "63646233127758", "315876691291677", "1570540515980274", "7821755377244303", "39014584984477092", "194880246951838595", "974725768600891269", "4881251640514912341", "24472502362094874818", "122826412768568196148", "617080993446201431307", "3103152024451536273288", "15618892303340118758816", "78679501136505611375745" ]

Number of fixed hexagonal polyominoes with n cells.

A001208

[ "3", "8", "15", "26", "35", "52", "69", "89", "112", "146", "172", "212", "259", "302", "354", "418", "476", "548", "633", "714", "805", "902", "1012", "1127", "1254", "1382", "1524", "1678", "1841", "2010", "2188", "2382", "2584", "2801", "3020", "3256", "3508", "3772", "4043", "4326", "4628", "4941", "5272", "5606", "5960", "6334", "6723", "7120" ]

a(n) = solution to the postage stamp problem with 3 denominations and n stamps.

A001209

[ "4", "12", "24", "44", "71", "114", "165", "234", "326", "427", "547", "708", "873", "1094", "1383", "1650", "1935", "2304", "2782", "3324", "3812", "4368", "5130", "5892", "6745", "7880", "8913", "9919", "11081", "12376", "13932", "15657", "17242", "18892", "21061", "23445", "25553", "27978", "31347", "33981", "36806", "39914", "43592" ]

a(n) is the solution to the postage stamp problem with 4 denominations and n stamps.

A001210

[ "5", "16", "36", "70", "126", "216", "345", "512", "797", "1055", "1475", "2047", "2659", "3403", "4422", "5629", "6865", "8669", "10835", "12903", "15785", "18801", "22456", "26469", "31108", "36949", "42744", "49436", "57033", "66771", "75558", "86303", "96852", "110253", "123954", "140688", "158389", "178811", "197293", "223580" ]

a(n) is the solution to the postage stamp problem with 5 denominations and n stamps.

A001211

[ "6", "20", "52", "108", "211", "388", "664", "1045", "1617", "2510", "3607", "5118", "7066", "9748", "12793", "17061", "22342", "28874", "36560", "45745", "57814", "72997", "87555", "106888", "129783" ]

a(n) is the solution to the postage stamp problem with 6 denominations and n stamps.

A001212

[ "2", "4", "8", "12", "16", "20", "26", "32", "40", "46", "54", "64", "72", "80", "92", "104", "116", "128", "140", "152", "164", "180", "196", "212" ]

a(n) = solution to the postage stamp problem with n denominations and 2 stamps.

A001213

[ "3", "7", "15", "24", "36", "52", "70", "93", "121", "154", "186", "225", "271", "323", "385", "450", "515", "606", "684", "788", "865", "977", "1091", "1201", "1361" ]

a(n) is the solution to the postage stamp problem with n denominations and 3 stamps.

A001214

[ "4", "10", "26", "44", "70", "108", "162", "228", "310", "422", "550", "700", "878", "1079", "1344", "1606", "1944", "2337", "2766", "3195", "3668", "4251", "4923", "5631", "6429" ]

a(n) is the solution to the postage stamp problem with n denominations and 4 stamps.

A001215

[ "5", "14", "35", "71", "126", "211", "336", "524", "726", "1016", "1393", "1871", "2494", "3196", "4063", "5113", "6511", "7949", "9865", "11589" ]

a(n) is the solution to the postage stamp problem with n denominations and 5 stamps.

A001216

[ "6", "18", "52", "114", "216", "388", "638", "1007", "1545", "2287" ]

a(n) = solution to the postage stamp problem with n denominations and 6 stamps.

A001217

[ "1", "2", "4", "6", "8", "12", "24", "48", "120", "192", "384", "720", "1152", "1920", "3840", "5040", "23040", "40320", "46080", "51840", "322560", "362880", "645120", "2903040", "3628800", "5160960", "10321920", "39916800", "92897280", "185794560", "479001600", "696729600", "1857945600", "3715891200" ]

Sorted list of orders of Weyl groups of types A_n, B_n, D_n, E_n, F_4, G_2.

A001218

[ "1", "3", "9", "27", "81", "43", "29", "87", "61", "83", "49", "47", "41", "23", "69", "7", "21", "63", "89", "67", "1", "3", "9", "27", "81", "43", "29", "87", "61", "83", "49", "47", "41", "23", "69", "7", "21", "63", "89", "67", "1", "3", "9", "27", "81", "43", "29", "87", "61", "83", "49", "47", "41", "23", "69", "7", "21", "63", "89", "67" ]

a(n) = 3^n mod 100.

A001219

[ "0", "6", "120", "210", "990", "185136", "258474216" ]

Triangular numbers of form a(a+1)(a+2).

A001220

[ "1093", "3511" ]

Wieferich primes: primes p such that p^2 divides 2^(p-1) - 1.

A001221

[ "0", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "1", "2", "2", "2", "2", "1", "2", "2", "2", "1", "3", "1", "2", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "2", "1", "3", "1", "2", "2", "1", "2", "3", "1", "2", "2", "3", "1", "2", "1", "2", "2", "2", "2", "3", "1", "2", "1", "2", "1", "3", "2", "2", "2", "2", "1", "3", "2", "2", "2", "2", "2", "2", "1", "2", "2", "2", "1", "3", "1", "2", "3", "2", "1", "2", "1", "3", "2" ]

Number of distinct primes dividing n (also called omega(n)).

A001222

[ "0", "1", "1", "2", "1", "2", "1", "3", "2", "2", "1", "3", "1", "2", "2", "4", "1", "3", "1", "3", "2", "2", "1", "4", "2", "2", "3", "3", "1", "3", "1", "5", "2", "2", "2", "4", "1", "2", "2", "4", "1", "3", "1", "3", "3", "2", "1", "5", "2", "3", "2", "3", "1", "4", "2", "4", "2", "2", "1", "4", "1", "2", "3", "6", "2", "3", "1", "3", "2", "3", "1", "5", "1", "2", "3", "3", "2", "3", "1", "5", "4", "2", "1", "4", "2", "2", "2", "4", "1", "4", "2", "3", "2", "2", "2", "6", "1", "3", "3", "4", "1", "3", "1", "4", "3", "2", "1", "5", "1", "3", "2" ]

Number of prime divisors of n counted with multiplicity (also called big omega of n, bigomega(n) or Omega(n)).

A001223

[ "1", "2", "2", "4", "2", "4", "2", "4", "6", "2", "6", "4", "2", "4", "6", "6", "2", "6", "4", "2", "6", "4", "6", "8", "4", "2", "4", "2", "4", "14", "4", "6", "2", "10", "2", "6", "6", "4", "6", "6", "2", "10", "2", "4", "2", "12", "12", "4", "2", "4", "6", "2", "10", "6", "6", "6", "2", "6", "4", "2", "10", "14", "4", "2", "4", "14", "6", "10", "2", "4", "6", "8", "6", "6", "4", "6", "8", "4", "8", "10", "2", "10", "2", "6", "4", "6", "8", "4", "2", "4", "12", "8", "4", "8", "4", "6", "12" ]

Prime gaps: differences between consecutive primes.

A001224

[ "1", "2", "2", "4", "5", "9", "12", "21", "30", "51", "76", "127", "195", "322", "504", "826", "1309", "2135", "3410", "5545", "8900", "14445", "23256", "37701", "60813", "98514", "159094", "257608", "416325", "673933", "1089648", "1763581", "2852242", "4615823", "7466468", "12082291", "19546175", "31628466" ]

If F(n) is the n-th Fibonacci number, then a(2n) = (F(2n+1) + F(n+2))/2 and a(2n+1) = (F(2n+2) + F(n+1))/2.

A001225

[ "1", "2", "5", "7", "11", "14", "20", "24", "30", "35", "44", "50" ]

Number of consistent arcs in a tournament with n nodes.

A001226

[ "1", "1", "3", "9", "7", "93", "315", "17", "3855", "13797", "195", "182361", "41943", "9709", "9256395", "34636833", "31775", "479349", "1857283155", "430185", "26817356775", "102280151421", "372827", "1497207322929", "89756051247", "84215045", "84973577874915", "19991120505", "1205604855", "4885260612740877" ]

Lerch's function q_2(n) = (2^{phi(t)} - 1)/t where t = 2*n - 1.

A001227

[ "1", "1", "2", "1", "2", "2", "2", "1", "3", "2", "2", "2", "2", "2", "4", "1", "2", "3", "2", "2", "4", "2", "2", "2", "3", "2", "4", "2", "2", "4", "2", "1", "4", "2", "4", "3", "2", "2", "4", "2", "2", "4", "2", "2", "6", "2", "2", "2", "3", "3", "4", "2", "2", "4", "4", "2", "4", "2", "2", "4", "2", "2", "6", "1", "4", "4", "2", "2", "4", "4", "2", "3", "2", "2", "6", "2", "4", "4", "2", "2", "5", "2", "2", "4", "4", "2", "4", "2", "2", "6", "4", "2", "4", "2", "4", "2", "2", "3", "6", "3", "2", "4", "2", "2", "8" ]

Number of odd divisors of n.

A001228

[ "7920", "95040", "175560", "443520", "604800", "10200960", "44352000", "50232960", "244823040", "898128000", "4030387200", "145926144000", "448345497600", "460815505920", "495766656000", "42305421312000", "64561751654400", "273030912000000", "51765179004000000", "90745943887872000", "4089470473293004800", "4157776806543360000", "86775571046077562880", "1255205709190661721292800", "4154781481226426191177580544000000", "808017424794512875886459904961710757005754368000000000" ]

Orders of sporadic simple groups.

A001229

[ "1", "2", "8", "12", "128", "240", "720", "6912", "32768", "142560", "712800", "1140480", "1190400", "3345408", "3571200", "5702400", "14859936", "29719872", "50319360", "118879488", "2147483648", "3889036800", "4389396480", "21946982400", "47416320000", "92177326080", "133145026560", "331914240000" ]

Numbers n such that phi(sigma(n)) = n.

A001230

[ "0", "0", "9862", "13267364410532" ]

Number of undirected closed knight's tours on a 2n X 2n chessboard.

A001231

[ "1", "1", "1", "1", "0", "1", "1", "4", "0" ]

Number of nonisomorphic projective planes of order n.

A001232

[ "1089", "10989", "109989", "1099989", "10891089", "10999989", "108901089", "109999989", "1089001089", "1098910989", "1099999989", "10890001089", "10989010989", "10999999989", "108900001089", "108910891089", "109890010989", "109989109989", "109999999989", "1089000001089", "1089109891089" ]

Numbers k such that 9*k = (k written backwards), k > 0.

A001233

[ "1", "21", "322", "4536", "63273", "902055", "13339535", "206070150", "3336118786", "56663366760", "1009672107080", "18861567058880", "369012649234384", "7551527592063024", "161429736530118960", "3599979517947607200", "83637381699544802976", "2021687376910682741568", "50779532534302850198976", "1323714091579185857760000" ]

Unsigned Stirling numbers of first kind s(n,6).

A001234

[ "1", "28", "546", "9450", "157773", "2637558", "44990231", "790943153", "14409322928", "272803210680", "5374523477960", "110228466184200", "2353125040549984", "52260903362512720", "1206647803780373360", "28939583397335447760" ]

Unsigned Stirling numbers of the first kind s(n,7).

A001235

[ "1729", "4104", "13832", "20683", "32832", "39312", "40033", "46683", "64232", "65728", "110656", "110808", "134379", "149389", "165464", "171288", "195841", "216027", "216125", "262656", "314496", "320264", "327763", "373464", "402597", "439101", "443889", "513000", "513856", "515375", "525824", "558441", "593047", "684019", "704977" ]

Taxi-cab numbers: sums of 2 cubes in more than 1 way.

A001236

[ "15", "575", "46760", "6998824", "1744835904", "673781602752", "381495483224064", "303443622431870976", "327643295527342080000", "466962174913357393920000", "858175477913267353681920000", "1993920215002599923346309120000", "5758788816015998806424467537920000" ]

Differences of reciprocals of unity.

A001237

[ "31", "3661", "1217776", "929081776", "1413470290176", "3878864920694016", "17810567950611972096", "129089983180418186674176", "1409795030885143760732160000", "22335321387514981111936450560000" ]

Differences of reciprocals of unity.

A001238

[ "63", "22631", "30480800", "117550462624", "1083688832185344", "21006340945438768128", "778101042571221893382144", "51150996584622542869024997376", "5626686079269855254796985958400000", "987233834003503822099304377378406400000" ]

Differences of reciprocals of unity.

A001239

[ "216", "251", "344", "729", "855", "1009", "1072", "1366", "1457", "1459", "1520", "1674", "1728", "1729", "1730", "1737", "1756", "1763", "1793", "1854", "1945", "2008", "2072", "2241", "2414", "2456", "2458", "2729", "2736", "2752", "3060", "3391", "3402", "3457", "3500", "3592", "3599", "3655", "3744", "3745" ]

Numbers that are the sum of 3 nonnegative cubes in more than 1 way.

A001240

[ "1", "11", "85", "575", "3661", "22631", "137845", "833375", "5019421", "30174551", "181222405", "1087861775", "6528756781", "39177307271", "235078159765", "1410511939775", "8463200647741", "50779591044791", "304678708005925" ]

Expansion of 1/((1-2x)(1-3x)(1-6x)).

A001241

[ "1", "50", "1660", "46760", "1217776", "30480800", "747497920", "18139003520", "437786795776", "10536798272000", "253246254177280", "6082300519393280", "146028165842661376", "3505313580591718400", "84135194495708938240", "2019336829962040279040" ]

Differences of reciprocals of unity.

A001242

[ "1", "274", "48076", "6998824", "929081776", "117550462624", "14500866102976", "1765130436471424", "213373597575314176", "25700650466807540224", "3089923562153380965376", "371145495540181143169024", "44558899569395347436056576", "5348360831598738338465357824" ]

Differences of reciprocals of unity.

A001243

[ "1", "247", "14608", "455192", "9738114", "162512286", "2275172004", "27971176092", "311387598411", "3207483178157", "31055652948388", "285997074307300", "2527925001876036", "21598596303099900", "179385804170146680" ]

Eulerian numbers (Euler's triangle: column k=7 of A008292, column k=6 of A173018).

A001244

[ "1", "502", "47840", "2203488", "66318474", "1505621508", "27971176092", "447538817472", "6382798925475", "83137223185370", "1006709967915228", "11485644635009424", "124748182104463860", "1300365805079109480", "13093713503185076040" ]

Eulerian numbers (Euler's triangle: column k=8 of A008292, column k=7 of A173018).

A001245

[ "81", "126", "128", "216", "217", "219", "224", "243", "251", "252", "259", "278", "280", "315", "341", "343", "344", "345", "352", "371", "376", "378", "405", "408", "432", "434", "467", "469", "496", "522", "540", "559", "560", "567", "584", "593", "594", "648", "687", "702", "728", "729", "730", "737", "756", "758", "763", "765", "783", "793", "802" ]

Numbers that are the sum of 4 cubes in more than 1 way.

A001246

[ "1", "1", "4", "25", "196", "1764", "17424", "184041", "2044900", "23639044", "282105616", "3455793796", "43268992144", "551900410000", "7152629313600", "93990019574025", "1250164827828900", "16807771574144100", "228138727737690000", "3123219182728976100", "43087676888260976400", "598598221893939680400", "8369059450146650049600" ]

Squares of Catalan numbers.

A001247

[ "1", "1", "4", "25", "225", "2704", "41209", "769129", "17139600", "447195609", "13450200625", "460457244900", "17754399678409", "764214897046969", "36442551140059684", "1912574337188517025", "109833379421325769609", "6866586647633870998416", "465228769500062060333281" ]

Squares of Bell numbers.

A001248

[ "4", "9", "25", "49", "121", "169", "289", "361", "529", "841", "961", "1369", "1681", "1849", "2209", "2809", "3481", "3721", "4489", "5041", "5329", "6241", "6889", "7921", "9409", "10201", "10609", "11449", "11881", "12769", "16129", "17161", "18769", "19321", "22201", "22801", "24649", "26569", "27889", "29929", "32041", "32761", "36481" ]

Squares of primes.

A001249

[ "1", "16", "100", "400", "1225", "3136", "7056", "14400", "27225", "48400", "81796", "132496", "207025", "313600", "462400", "665856", "938961", "1299600", "1768900", "2371600", "3136441", "4096576", "5290000", "6760000", "8555625", "10732176", "13351716", "16483600", "20205025", "24601600", "29767936", "35808256" ]

Squares of tetrahedral numbers: a(n) = binomial(n+3,n)^2.

A001250

[ "1", "1", "2", "4", "10", "32", "122", "544", "2770", "15872", "101042", "707584", "5405530", "44736512", "398721962", "3807514624", "38783024290", "419730685952", "4809759350882", "58177770225664", "740742376475050", "9902996106248192", "138697748786275802", "2030847773013704704", "31029068327114173810" ]

Number of alternating permutations of order n.

A001251

[ "0", "0", "2", "12", "70", "442", "3108", "24216", "208586", "1972904", "20373338", "228346522", "2763212980", "35926266244", "499676669254", "7405014187564", "116511984902094", "1940073930857802", "34087525861589564", "630296344519286304", "12235215845125112122", "248789737587365945992" ]

Number of permutations of order n with the length of longest run equal 3.

A001252

[ "0", "0", "0", "2", "16", "134", "1164", "10982", "112354", "1245676", "14909340", "191916532", "2646100822", "38932850396", "609137502242", "10101955358506", "177053463254274", "3270694371428814", "63524155236581118", "1294248082658393546", "27604013493657933856", "615135860462018980316" ]

Number of permutations of order n with the length of longest run equal 4.

A001253

[ "0", "0", "0", "0", "2", "20", "198", "2048", "22468", "264538", "3340962", "45173518", "652209564", "10024669626", "163546399460", "2823941647390", "51468705947590", "987671243816650", "19909066390361346", "420650676776338140", "9297308938203169622", "214562999510569012168" ]

Number of permutations of order n with the length of longest run equal 5.

A001254

[ "4", "1", "9", "16", "49", "121", "324", "841", "2209", "5776", "15129", "39601", "103684", "271441", "710649", "1860496", "4870849", "12752041", "33385284", "87403801", "228826129", "599074576", "1568397609", "4106118241", "10749957124", "28143753121", "73681302249", "192900153616", "505019158609", "1322157322201", "3461452808004", "9062201101801", "23725150497409" ]

Squares of Lucas numbers.

A001255

[ "1", "1", "4", "9", "25", "49", "121", "225", "484", "900", "1764", "3136", "5929", "10201", "18225", "30976", "53361", "88209", "148225", "240100", "393129", "627264", "1004004", "1575025", "2480625", "3833764", "5934096", "9060100", "13823524", "20839225", "31404816", "46812964", "69705801", "102880449", "151536100" ]

Squares of partition numbers.

A001256

[ "1", "1", "1", "1", "4", "9", "36", "121", "529", "2209", "11236", "55225", "303601", "1692601", "9979281", "59923081", "373262400", "2364779641", "15343033689", "101095382025", "677435994225", "4598901695025", "31626631547536", "219871778549476", "1544481904210609", "10948878748872100", "78284374662902500" ]

Squares of numbers of trees.

A001257

[ "1", "1", "4", "16", "81", "400", "2304", "13225", "81796", "516961", "3392964", "22714756", "155900196", "1087218729", "7710771721", "55404215161", "403030713409", "2962388303281", "21983682632976", "164512124707984", "1240577449436224" ]

Squares of numbers of rooted trees.

A001258

[ "1", "1", "2", "6", "25", "135", "892", "6937", "61886", "621956", "6946471", "85302935", "1141820808", "16540534553", "257745010762", "4298050731298", "76356627952069", "1439506369337319", "28699241994332940", "603229325513240569", "13330768181611378558", "308967866671489907656", "7493481669479297191451", "189793402599733802743015", "5010686896406348299630712" ]

Number of labeled n-node trees with unlabeled end-points.

A001259

[ "3", "5", "7", "17", "19", "37", "97", "113", "257", "401", "487", "631", "971", "1297", "1801", "19457", "22051", "28817", "65537", "157303", "160001" ]

A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.

A001260

[ "0", "0", "0", "0", "1", "5", "45", "385", "3710", "38934", "444990", "5506710", "73422855", "1049946755", "16035550531", "260577696015", "4489954146860", "81781307674780", "1570201107355980", "31698434854748604", "671260973394676605", "14879618243581997745" ]

Number of permutations of length n with 4 consecutive ascending pairs.

A001261

[ "0", "0", "0", "0", "0", "1", "6", "63", "616", "6678", "77868", "978978", "13216104", "190899423", "2939850914", "48106651593", "833848627248", "15265844099324", "294412707629208", "5966764207952724", "126793739418994416", "2819296088257641741", "65470320271760790078" ]

Number of permutations of length n with 5 consecutive ascending pairs.

A001262

[ "2047", "3277", "4033", "4681", "8321", "15841", "29341", "42799", "49141", "52633", "65281", "74665", "80581", "85489", "88357", "90751", "104653", "130561", "196093", "220729", "233017", "252601", "253241", "256999", "271951", "280601", "314821", "357761", "390937", "458989", "476971", "486737" ]

Strong pseudoprimes to base 2.

A001263

[ "1", "1", "1", "1", "3", "1", "1", "6", "6", "1", "1", "10", "20", "10", "1", "1", "15", "50", "50", "15", "1", "1", "21", "105", "175", "105", "21", "1", "1", "28", "196", "490", "490", "196", "28", "1", "1", "36", "336", "1176", "1764", "1176", "336", "36", "1", "1", "45", "540", "2520", "5292", "5292", "2520", "540", "45", "1", "1", "55", "825", "4950", "13860", "19404", "13860", "4950", "825" ]

Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.

A001264

[ "1", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96", "84", "36", "44", "76", "4", "16", "64", "56", "24", "96" ]

Final 2 digits of 4^n.

A001265

[ "0", "1", "3", "7", "3", "5", "31", "3", "3", "7", "127", "3", "5", "17", "7", "73", "3", "11", "31", "23", "89", "3", "3", "5", "7", "13", "8191", "3", "43", "127", "7", "31", "151", "3", "5", "17", "257", "131071", "3", "3", "3", "7", "19", "73", "524287", "3", "5", "5", "11", "31", "41", "7", "7", "127", "337", "3", "23", "89", "683", "47", "178481", "3", "3", "5", "7", "13", "17", "241" ]

Table T(n,k) in which n-th row lists prime factors of 2^n - 1 (n >= 2), with repetition.

A001266

[ "0", "0", "1", "7", "45", "323", "2621", "23811", "239653", "2648395", "31889517", "415641779", "5830753109", "87601592187", "1403439027805", "23883728565283", "430284458893701", "8181419271349931", "163730286973255373", "3440164703027845395", "75718273707281368117", "1742211593431076483419" ]

One-half the number of permutations of length n without rising or falling successions.

A001267

[ "0", "0", "0", "0", "1", "8", "60", "444", "3599", "32484", "325322", "3582600", "43029621", "559774736", "7841128936", "117668021988", "1883347579515", "32026067455084", "576605574327174", "10957672400252944", "219190037987444577", "4603645435776504120", "101292568208941883236", "2329975164242735146316" ]

One-half the number of permutations of length n with exactly 3 rising or falling successions.

A001268

[ "0", "0", "0", "0", "0", "1", "11", "113", "1099", "11060", "118484", "1366134", "16970322", "226574211", "3240161105", "49453685911", "802790789101", "13815657556958", "251309386257874", "4818622686395380", "97145520138758844", "2054507019515346789", "45484006970415223287", "1052036480881734378541" ]

One-half the number of permutations of length n with exactly 4 rising or falling successions.

A001269

[ "2", "3", "5", "3", "3", "17", "3", "11", "5", "13", "3", "43", "257", "3", "3", "3", "19", "5", "5", "41", "3", "683", "17", "241", "3", "2731", "5", "29", "113", "3", "3", "11", "331", "65537", "3", "43691", "5", "13", "37", "109", "3", "174763", "17", "61681", "3", "3", "43", "5419", "5", "397", "2113", "3", "2796203", "97", "257", "673", "3", "11", "251", "4051" ]

Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), with repetition.

A001270

[ "3", "3", "3", "3", "11", "3", "3", "3", "37", "3", "3", "11", "101", "3", "3", "41", "271", "3", "3", "3", "7", "11", "13", "37", "3", "3", "239", "4649", "3", "3", "11", "73", "101", "137", "3", "3", "3", "3", "37", "333667", "3", "3", "11", "41", "271", "9091", "3", "3", "21649", "513239", "3", "3", "3", "7", "11", "13", "37", "101", "9901", "3", "3", "53", "79", "265371653" ]

Table of prime factors of 10^n - 1 (with multiplicity).

A001271

[ "2", "11", "101", "7", "11", "13", "73", "137", "11", "9091", "101", "9901", "11", "909091", "17", "5882353", "7", "11", "13", "19", "52579", "101", "3541", "27961", "11", "11", "23", "4093", "8779", "73", "137", "99990001", "11", "859", "1058313049", "29", "101", "281", "121499449", "7", "11", "13", "211", "241", "2161", "9091", "353", "449", "641", "1409", "69857" ]

Irregular table read by rows: row n lists prime factors of 10^n +1, with multiplicity.

A001272

[ "3", "4", "5", "6", "7", "8", "10", "15", "19", "41", "59", "61", "105", "160", "661", "2653", "3069", "3943", "4053", "4998", "8275", "9158", "11164", "43592", "59961" ]

Numbers k such that k! - (k-1)! + (k-2)! - (k-3)! + ... - (-1)^k*1! is prime.

A001273

[ "1", "10", "13", "23", "19", "7", "356", "78999" ]

Smallest number that takes n steps to reach 1 under iteration of sum-of-squares-of-digits map (= smallest "happy number" of height n).

A001274

[ "1", "3", "15", "104", "164", "194", "255", "495", "584", "975", "2204", "2625", "2834", "3255", "3705", "5186", "5187", "10604", "11715", "13365", "18315", "22935", "25545", "32864", "38804", "39524", "46215", "48704", "49215", "49335", "56864", "57584", "57645", "64004", "65535", "73124", "105524", "107864", "123824", "131144", "164175", "184635" ]

Numbers k such that phi(k) = phi(k+1).

A001275

[ "3", "7", "23", "61", "127", "199", "337", "479", "677", "937", "1193", "1511", "1871", "2267", "2707", "3251", "3769", "4349", "5009", "5711", "6451", "7321", "8231", "9173", "10151", "11197", "12343", "13487", "14779", "16097", "17599", "19087", "20563", "22109", "23761", "25469", "27259", "29123", "31081", "33029" ]

Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2.

A001276

[ "2", "3", "7", "15", "27", "41", "62", "85", "115", "150", "186", "229", "274", "323", "380", "443", "509", "577", "653", "733", "818", "912", "1010", "1114", "1222", "1331", "1448", "1572", "1704", "1845", "1994", "2138", "2289", "2445", "2609", "2774", "2948", "3127", "3311", "3502", "3699", "3900", "4112", "4324", "4546", "4775", "5016", "5255", "5493" ]

Smallest k such that the product of q/(q-1) over the primes from prime(n) to prime(n+k-1) is greater than 2.

A001277

[ "1", "3", "12", "56", "321", "2175", "17008", "150504", "1485465", "16170035", "192384876", "2483177808", "34554278857", "515620794591", "8212685046336", "139062777326000", "2494364438359953", "47245095998005059", "942259727190907180", "19737566982241851720", "433234326593362631601", "9943659797649140568863" ]