Datasets:
christopher
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oeis

Dataset card Data Studio Files Community
a-number
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852
A000801
[ "2", "4", "6", "10", "16", "26", "44", "76", "132", "234", "420", "761", "1391", "2561", "4745", "8841", "16551", "31114", "58708", "111136", "211000", "401650", "766372", "1465422", "2807599", "5388709", "10359735", "19946715", "38459505", "74250899", "143524565", "277742293", "538043341", "1043333611", "2025040421" ]
a(n) = Sum_{k = 1..n} floor(2^k / k).
A000802
[ "1", "2", "4", "7", "11", "19", "34", "50", "82", "146", "274", "529", "785", "1297", "2321", "4369", "8465", "16657", "33041", "65809", "131344", "196880", "327952", "590096", "1114384", "2162960", "4260112", "8454416", "16843024", "33620240", "67174672", "134283536", "268501264", "536936720", "1073807632", "2147549456", "4295033104" ]
Maximal number of states in the minimal deterministic finite automaton accepting a language over a binary alphabet consisting of some words of length n.
A000803
[ "0", "0", "8", "4", "8", "16", "24", "44", "80", "144", "264", "484", "888", "1632", "3000", "5516", "10144", "18656", "34312", "63108", "116072", "213488", "392664", "722220", "1328368", "2443248", "4493832", "8265444", "15202520", "27961792", "51429752", "94594060", "173985600", "320009408" ]
a(n+3) = a(n+2) + a(n+1) + a(n) - 4.
A000804
[ "1", "1", "2", "6", "24", "120", "265", "579", "1265", "2783", "6208", "13909", "31337", "70985", "161545", "369024", "845825", "1944295", "4480285", "10345391", "23930320", "55435605", "128577253", "298529333", "693718721", "1613210120", "3753680073", "8738534315", "20351593033", "47413960239", "110493496000" ]
Permanent of a certain cyclic n X n (0,1) matrix.
A000805
[ "1", "1", "2", "6", "24", "120", "720", "1854", "4738", "12072", "30818", "79118", "204448", "528950", "1370674", "3557408", "9244418", "24043990", "62573616", "162925614", "424377730", "1105703640", "2881483458", "7510389278", "19577689120", "51038756326", "133066443346", "346944079632", "904622495746", "2358783572710", "6150613767440", "16038217209886" ]
Permanent of a certain cyclic n X n (0,1) matrix.
A000806
[ "1", "0", "1", "-5", "36", "-329", "3655", "-47844", "721315", "-12310199", "234615096", "-4939227215", "113836841041", "-2850860253240", "77087063678521", "-2238375706930349", "69466733978519340", "-2294640596998068569", "80381887628910919255", "-2976424482866702081004", "116160936719430292078411" ]
Bessel polynomial y_n(-1).
A000807
[ "1", "2", "14", "182", "3614", "99302", "3554894", "159175382", "8654995454", "558786468422", "42086200603694", "3645412584724022", "358877175474325214", "39758874175808713382", "4915216680878167372814", "673139563824188490513302", "101475126400695241802946494", "16744618803625299734467026182" ]
Quadratic invariants.
A000808
[ "10", "76", "8416", "268496896", "576460756464173056", "5316911983139663509773741938679218176", "904625697166532776746648320380374280441295666129685538275829368373028847616" ]
Number of switching networks (see Harrison reference for precise definition).
A000809
[ "36", "1072", "2100736", "17592201773056", "2475880078571033228681936896", "98079714615416886934934209815610010226578261138395365376" ]
Number of switching networks (see Harrison reference for precise definition).
A000810
[ "1", "1", "8", "26", "352", "1936", "38528", "297296", "7869952", "78098176", "2583554048", "31336418816", "1243925143552", "17831101321216", "825787662368768", "13658417358350336", "722906928498737152", "13551022195053101056" ]
Expansion of e.g.f. (sin x + cos x)/cos 3x.
A000811
[ "16", "160", "13056", "183305216", "153746461690757120", "472614400151965797795362900461748224", "22974620880419880070513913016918297106276186594558904213019777370224066560" ]
Number of switching networks (see Harrison reference for precise definition).
A000812
[ "64", "2304", "2928640", "11745443774464", "660235081293571848291745792", "8718196854704187882046649324045198931057057476097605632" ]
Number of switching networks (see Harrison reference for precise definition).
A000813
[ "1", "1", "15", "47", "1185", "6241", "230895", "1704527", "83860545", "796079041", "48942778575", "567864586607", "41893214676705", "574448847467041", "49441928730798255", "782259922208550287", "76946148390480577665", "1379749466246228538241" ]
Expansion of (sin x + cos x)/cos 4x.
A000814
[ "10", "55", "1996", "11756666", "4805323147589984", "7384600028168436080716029918923776", "179489225628280313255222684940441967551973345417569571214806075240914944" ]
Number of switching networks (see Harrison reference for precise definition).
A000815
[ "36", "666", "384112", "735192450952", "20632358601785638477436416", "136221825854760195018034839832322234167109566010687488" ]
Number of switching networks (see Harrison reference for precise definition).
A000816
[ "0", "2", "40", "1952", "177280", "25866752", "5535262720", "1633165156352", "635421069967360", "315212388819402752", "194181169538675507200", "145435130631317935357952", "130145345400688287667978240", "137139396592145493713802493952" ]
E.g.f.: Sum_{n >= 0} a(n) * x^(2*n) / (2*n)! = sin(x)^2 / cos(2*x).
A000817
[ "16", "80", "1056", "320416", "1858620869536", "16880173675357998942609488800", "706695723125809149019144715477884710572926078237246360174451424" ]
Number of switching networks under action of GL_n(Z_2).
A000818
[ "64", "960", "135040", "14333211520", "7923543700147758911104", "311384101966962110823277061581833720077525851776" ]
Number of switching networks under action of GL_n(Z_2).
A000819
[ "1", "2", "40", "1952", "177280", "25866752", "5535262720", "1633165156352", "635421069967360", "315212388819402752", "194181169538675507200", "145435130631317935357952", "130145345400688287667978240", "137139396592145493713802493952" ]
E.g.f.: cos(x)^2 / cos(2x) = Sum_{n >= 0} a(n) * x^(2n) / (2n)!.
A000820
[ "10", "35", "271", "29821", "58561146596", "263752834000960467258171320", "5521060336920386371390128802363265964201729623531400218908632" ]
Number of switching networks under action of AG_n(Z_2).
A000821
[ "36", "330", "22060", "920737780", "247617673784972437216", "4865376593267541575898325655326600134256578720" ]
Number of switching networks under action of AG_n(Z_2).
A000822
[ "0", "1", "2", "11", "40", "361", "1952", "24611", "177280", "2873041", "25866752", "512343611", "5535262720", "129570724921", "1633165156352", "44110959165011", "635421069967360", "19450718635716001", "315212388819402752", "10784052561125704811" ]
Expansion of (sin^2 x + sin x) /cos 2x.
A000823
[ "7", "46", "4336", "134281216", "288230380379570176", "2658455991569831764110243006194384896", "452312848583266388373324160190187140390789016525312000869601987902398529536" ]
Number of switching networks (see Harrison reference for precise definition).
A000824
[ "13", "237", "356026", "2932175712336", "412646680050205587085305856", "16346619102569481158480824333166611354489546429742186496" ]
Number of switching networks (see Harrison reference for precise definition).
A000825
[ "1", "1", "3", "8", "57", "256", "2763", "17408", "250737", "2031616", "36581523", "362283008", "7828053417", "91620376576", "2309644635483", "31191159799808", "898621108880097", "13753735117275136", "445777636063460643", "7625476699018231808" ]
Expansion of cos x (1 + sin x ) /cos 2x.
A000826
[ "10", "88", "6616", "91666432", "76873231310808704", "236307200075982899871259747594698752", "11487310440209940035256956508459148560969989043872580978940882909553754112", "166267459448692920381622333807116147427859895760062485070882091322892520958706179582178218311954136674872641052328937320550635171107567787263574147072" ]
Number of switching networks (see Harrison reference for precise definition).
A000827
[ "20", "484", "497760", "1957701217328", "110039180295740617586514688", "1453032809117364647244136820047121806179196309892169728" ]
Number of switching networks (see Harrison reference for precise definition).
A000828
[ "1", "1", "2", "8", "40", "256", "1952", "17408", "177280", "2031616", "25866752", "362283008", "5535262720", "91620376576", "1633165156352", "31191159799808", "635421069967360", "13753735117275136", "315212388819402752", "7625476699018231808" ]
E.g.f. cos(x)/(cos(x) - sin(x)).
A000829
[ "7", "34", "1056", "5884954", "2402661748356256", "3692300014084218317379484106943488", "89744612814140156627611342470220985493433638691231381252948710213328896" ]
Number of switching networks (see Harrison reference for precise definition).
A000830
[ "13", "158", "66336", "122544034314", "3438726436264160394888822", "22703637642460032506699838997723739937009913804573344" ]
Number of switching networks (see Harrison reference for precise definition).
A000831
[ "1", "2", "4", "16", "80", "512", "3904", "34816", "354560", "4063232", "51733504", "724566016", "11070525440", "183240753152", "3266330312704", "62382319599616", "1270842139934720", "27507470234550272", "630424777638805504", "15250953398036463616", "388362339077351014400", "10384044045105304174592" ]
Expansion of e.g.f. (1 + tan(x))/(1 - tan(x)).
A000832
[ "10", "46", "556", "160948", "929312039044", "8440086837679170219118159556", "353347861562904574509572357738975845669311200577543225891351084" ]
Number of switching networks (see Harrison reference for precise definition).
A000833
[ "20", "220", "23932", "2390065448", "1320590620757744871288", "51897350327827018479313921072100496772300552736" ]
Number of switching networks (see Harrison reference for precise definition).
A000834
[ "1", "3", "9", "35", "177", "1123", "8569", "76355", "777697", "8911683", "113466729", "1589173475", "24280777617", "401898209443", "7163977596889", "136821894075395", "2787312733887937", "60331585563062403", "1382698089425999049" ]
Expansion of exp(x)*(1 + tan(x))/(1 - tan(x)).
A000835
[ "7", "22", "153", "15209", "29281010032", "131876417000509741750888020", "2760530168460193185695064401186144339478505237725915631330140" ]
Number of switching networks (see Harrison reference for precise definition).
A000836
[ "13", "87", "4148", "153668757", "41269612629126375351", "810896098877923596128062174904361421866219158" ]
Number of switching networks (see Harrison reference for precise definition).
A000837
[ "1", "1", "1", "2", "3", "6", "7", "14", "17", "27", "34", "55", "63", "100", "119", "167", "209", "296", "347", "489", "582", "775", "945", "1254", "1481", "1951", "2334", "2980", "3580", "4564", "5386", "6841", "8118", "10085", "12012", "14862", "17526", "21636", "25524", "31082", "36694", "44582", "52255", "63260", "74170", "88931", "104302" ]
Number of partitions of n into relatively prime parts. Also aperiodic partitions.
A000838
[ "4", "28", "2272", "67170304", "144115192236605440", "1329227995784915891062320757838184448", "226156424291633194186662080095093570363541849729447858357132587076662853632" ]
Number of n-input 2-output switching networks under action of complementing group on the inputs and outputs.
A000839
[ "8", "176", "265728", "2199038984192", "309485009821617747608469504", "12259964326927110866866776295192695943928870296113643520" ]
Number of n-input 3-output switching networks under action of complementing group on the inputs and outputs.
A000840
[ "0", "0", "1", "1", "2", "5", "12", "31", "90", "285", "938", "3285", "11983", "45390", "177803", "718390", "2986407", "12749364", "55802982", "250068732", "1145923828", "5363795830", "25620207380", "124767647097", "618983876918", "3126035142910", "16060182735947", "83883575376862", "445164927249466", "2399098651337048" ]
Number of cubic bicolored graphs on n unlabeled nodes admitting an automorphism exchanging the colors.
A000841
[ "4", "40", "3264", "45826304", "38436615422689280", "118153600037991449448840725115437056", "5743655220104970017628478254229574276569046648639726053254944342556016640" ]
Number of n-input 2-output switching networks under action of symmetric group S(n) on the inputs and complementing group C(2,2) on the outputs.
A000842
[ "8", "288", "366080", "1468180471808", "82529385161696481036468224", "1089774606838023485255831165505649866382132184512200704" ]
Number of n-input 3-output switching networks under action of symmetric group S(n) on the inputs and complementing group C(3,2) on the outputs.
A000843
[ "0", "0", "0", "1", "1", "4", "12", "66", "433", "3442", "30404", "294951", "3093770", "34846185", "419020738", "5355289843", "72466668921", "1034818990771", "15548633703424", "245182764121059", "4047990858838185", "69826392559499108", "1256005988628521464", "23517396850332614602", "457623646061902648705" ]
Number of quartic bicolored graphs on n unlabeled nodes admitting an automorphism exchanging the colors.
A000844
[ "4", "19", "556", "2945786", "1201330980739424", "1846150007042109336331740689419264", "44872306407070078313805671235110493948692333391216774983943586135973888" ]
Number of switching networks (see Harrison reference for precise definition).
A000845
[ "8", "106", "49008", "91901007752", "2579044825238020792325632", "17027728231845024377254356563216673341241082335920128", "7634627316699699128123263912340182782717075954250211317249456247129155629314608610294934410743206996562935808" ]
Number of switching networks (see Harrison reference for precise definition).
A000846
[ "0", "1", "9", "64", "425", "2751", "17640", "112848", "722601", "4638205", "29860259", "192831288", "1248973544", "8112024844", "52820112480", "344712308064", "2254247833257", "14768735480505", "96917273443305", "636948624057900", "4191706659276675", "27618897144488595", "182181063882796680" ]
a(n) = C(3n,n) - C(2n,n).
A000847
[ "4", "20", "264", "80104", "464655217384", "4220043418839499735652372200", "176673930781452287254786178869471177643231519559311590043612856" ]
Number of n-input 2-output switching networks under action of GL(n,2) on the inputs and complementing group C(2,2) on the outputs.
A000848
[ "8", "120", "16880", "1791651440", "990442962518469863888", "38923012745870263852909632697729215009690731472" ]
Number of n-input 3-output switching networks under action of GL(n,2) on the inputs and complementing group C(3,2) on the outputs.
A000849
[ "0", "1", "3", "10", "46", "343", "3248", "42331", "646029", "12283531", "300369796", "8028643010", "259488750744", "9414916809095", "362597750396740", "15397728527812858", "742238179058722891", "40068968501510691894", "2251262473052300960826", "139566579945945392719413" ]
Number of primes <= product of first n primes, A002110(n).
A000850
[ "4", "11", "79", "7621", "14640634220", "65938208500258353412694720", "1380265084230096592847532200594565116571730065652126434152304" ]
Number of n-input 2-output switching networks under action of AG(n,2) on the inputs and complementing group C(2,2) on the outputs.
A000851
[ "8", "50", "2908", "115125476", "30952209248265753648", "608172074158442696987382009681097839529937904" ]
Number of n-input 3-output switching networks under action of AG(n,2) on the inputs and complementing group C(3,2) on the outputs.
A000852
[ "1", "8", "11", "18", "80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "120", "121", "122", "123", "124", "125", "126", "127", "128", "129", "130", "131", "132" ]
Numbers beginning with a vowel in English.
A000853
[ "3", "18", "1200", "33601536", "72057597192044544", "664613997892457950142846397346480128", "113078212145816597093331040047546785266841516594958545044409945396273479680" ]
Number of n-input 2-output switching networks under action of complementing group C(2,n) on inputs and S(2) and C(2,2) on outputs.
A000854
[ "4", "51", "46218", "366543984720", "51580835042395388382652416", "2043327387821185145142410066588796212566159639921557504" ]
Number of n-input 3-output switching networks under action of complementing group C(2,n) on inputs and S(3) and C(2,3) on outputs
A000855
[ "1", "2", "4", "8", "16", "32", "64", "28", "56", "12", "24", "48", "96", "92", "84", "68", "36", "72", "44", "88", "76", "52", "4", "8", "16", "32", "64", "28", "56", "12", "24", "48", "96", "92", "84", "68", "36", "72", "44", "88", "76", "52", "4", "8", "16", "32", "64", "28", "56", "12", "24", "48", "96", "92", "84", "68", "36", "72", "44", "88", "76", "52", "4", "8", "16", "32", "64", "28" ]
Final two digits of 2^n.
A000856
[ "3", "24", "1676", "22920064", "19218307944059712", "59076800018995725211209511239630848", "2871827610052485008814239127114787142200471197616427462842969283498868736" ]
Number of n-input 2-output switching networks under the action of S(n) on the inputs and S(2) and complementing group C(2,2) on the outputs
A000857
[ "4", "74", "63440", "244728561176", "13754897546985740953546112", "181629101139670580935062344094172140654053010592464896" ]
Number of n-input 3-output switching networks under the action of S(n) on the inputs and S(3) and complementing group C(2,3) on the outputs.
A000858
[ "0", "1", "4", "31", "293", "3326", "44189", "673471", "11588884", "222304897", "4704612119" ]
Duplicate of A003436.
A000859
[ "3", "13", "308", "1476218", "600665577652576", "923075003521054806676605033098240", "22436153203535039156902835617555247833069649686831685624592283895635968" ]
Number of n-input 2-output switching networks under action of S(n) and complementing group C(2,2) on inputs and outputs.
A000860
[ "4", "34", "8900", "15320103918", "429840804866758538021686", "2837954705307504063799234409931200916180905873402528" ]
Number of n-input 3-output switching networks under action of S(n) and complementing group C(2,3) on inputs and outputs.
A000861
[ "0", "1", "2", "3", "5", "9", "12", "21", "22", "23", "25", "29", "31", "32", "33", "35", "39", "41", "42", "43", "45", "49", "51", "52", "53", "55", "59", "61", "62", "63", "65", "69", "71", "72", "73", "75", "79", "81", "82", "83", "85", "89", "91", "92", "93", "95", "99", "101", "102", "103", "105", "109", "112", "121", "122", "123", "125", "129", "131", "132", "133", "135", "139", "141", "142" ]
Numbers ending with a vowel in American English.
A000862
[ "3", "8", "49", "3963", "7320535610", "32969104250143930769244222", "690132542115048296423766100299538236974685246850905568050026" ]
Number of n-input 2-output switching networks under action of AG(n,2) and complementing group C(2,2) on inputs and outputs.
A000863
[ "4", "19", "632", "19245637", "5158701627878530987", "101362012359740449534162019620212891642247346" ]
Number of n-input 3-output switching networks under action of AG(n,2) and complementing group C(2,3) on inputs and outputs
A000864
[ "91", "259", "451", "481", "703", "1729", "2821", "2981", "3367", "4141", "4187", "5461", "6533", "6541", "6601", "7471", "7777", "8149", "8401", "8911", "10001", "11111", "12403", "13981", "14701", "14911", "15211", "15841", "19201", "21931", "22321", "24013", "24661", "27613", "29341", "34133" ]
Deceptive nonprimes: composite numbers k that divide the repunit R_{k-1}.
A000865
[ "1", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "120", "121", "122", "123", "124", "125", "126", "127", "128", "129", "130", "131", "132", "133", "134", "135" ]
Numbers beginning with letter 'o' in English.
A000866
[ "1", "2", "4", "13", "31", "112", "224", "1003", "2011", "4022", "13044", "31143", "112341", "230232", "1011014", "2022033", "4044121", "13143242", "31342034", "113234123", "232023301", "1014102102", "2033204204", "4121413413", "13243332331", "32042220212", "114134440424", "233324431403", "1022204413311" ]
2^n written in base 5.
A000867
[ "4", "5", "14", "15", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "400", "401", "402", "403", "404", "405", "406", "407", "408", "409", "410", "411", "412", "413", "414", "415", "416", "417", "418", "419", "420" ]
Numbers beginning with letter 'f' in English.
A000868
[ "4", "21", "1531", "44782251", "96076794891512491", "886151997189943927518995693301312171", "150770949527755462791108053396729046910357127815416821444325531778055580331" ]
Number of switching networks with C(2,n) acting on domain and GL(2,Z2) acting on range.
A000869
[ "4", "27", "14056", "104751025086", "14737381492157353997140846", "583807825091767184801127161305581049499763751729421166" ]
Number of switching networks with C(2,n) acting on domain and GL(3,Z2) acting on range.
A000870
[ "6", "7", "16", "17", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79", "600", "601", "602", "603", "604", "605", "606", "607", "608", "609", "610", "611", "612", "613", "614", "615", "616", "617", "618", "619", "620" ]
Numbers beginning with letter 's' in English.
A000871
[ "5", "35", "2266", "30564722", "25624410747226866", "78769066691994300606138801216143967", "3829103480069980011752318836153049525544593512352968628868212239132475999" ]
Number of switching networks with S(n) acting on the domain and GL(2,2) acting on the range.
A000872
[ "5", "46", "19930", "69945183326", "3929970742021874526325166", "51894028897048737452225300581594776441516899880213358" ]
Number of switching networks with S(n) acting on the domain and GL(3,2) acting on the range.
A000873
[ "8", "11", "18", "80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "800", "801", "802", "803", "804", "805", "806", "807", "808", "809", "810", "811", "812", "813", "814", "815", "816", "817", "818", "819", "820", "821", "822", "823", "824", "825", "826", "827", "828", "829" ]
Numbers beginning with letter 'e' in English.
A000874
[ "4", "16", "392", "1966074", "800887365826790", "1230766671361406290474145896188319", "29914870938046718875870447490073662976109190218710989290080175747776895" ]
Number of switching networks with S(n) and C(2,2) acting on the domain and GL(2,2) acting on the range.
A000875
[ "4", "21", "2914", "4379140552", "122811659002267408721700", "810844201516429733173715469705141125645071310611982" ]
Number of switching networks with S(n) and C(2,2) acting on the domain and GL(3,2) acting on the range.
A000876
[ "1", "1", "0", "0", "3", "3", "0", "0", "1", "0", "1", "1", "2", "0", "7", "7", "0", "2", "1", "1", "0", "1", "2", "2", "3", "0", "3", "6", "10", "0", "13", "2", "9", "3", "10", "0", "15", "15", "0", "10", "3", "9", "2", "13", "0", "10", "6", "3", "0", "3", "2", "2", "5", "2", "25", "1", "42", "12", "7", "0", "7", "28", "170", "1", "217", "10", "37", "1" ]
From a self-replicating tiling.
A000877
[ "5", "20", "206", "54155", "309771751363", "2813362279226503905263636259", "117782620520968191503190785913014275478335890027037842956986579" ]
Number of switching networks with GL(n,2) acting on the domain and GL(2,2) acting on the range.
A000878
[ "5", "27", "1204", "85617952", "47163951612740818544", "1853476797422393518997156640106964554652232210", "1431405317608062035603436602561550164804819376613495652537557566563513965206452741153347013992258358" ]
Number of switching networks with GL(n,2) acting on the domain and GL(2,2) acting on the range.
A000879
[ "2", "4", "9", "15", "30", "39", "61", "72", "99", "146", "162", "219", "263", "283", "329", "409", "487", "519", "609", "675", "705", "811", "886", "1000", "1163", "1252", "1294", "1381", "1423", "1523", "1877", "1976", "2141", "2190", "2489", "2547", "2729", "2915", "3043", "3241", "3436", "3512", "3868", "3945", "4089", "4164", "4627", "5106" ]
Number of primes < prime(n)^2.
A000880
[ "4", "11", "64", "5276", "9760628902", "43958805666856252758341426", "920176722820064395231688133731722351411281463557094398071921" ]
Number of switching networks with AG(n,2) acting on the domain and GL(2,2) acting on the range.
A000881
[ "4", "15", "276", "5534533", "1473914807822315239", "28960574959925842749932484608400325311784104", "11182854043812984653151849586832952714557996202582672732591909323787317314909793862964567968430394" ]
Number of switching networks with AG(n,2) acting on the domain and GL(3,2) acting on the range.
A000882
[ "0", "1", "4", "15", "69", "468", "4636", "57453", "896062", "18463713", "425177757", "11997649372", "385088898632", "13280323588034", "509456736126003" ]
Number of twin prime pairs <= product of first n primes.
A000883
[ "2", "9", "443", "11211435", "24019199779842731", "221537999297485986455406144733751979", "37692737381938865697777013349182261812327566685142592258699083037385861803" ]
Number of switching networks with C(2,n) acting on the domain and AG(2,2) acting on the range.
A000884
[ "2", "10", "2104", "13098898366", "1842172695541070949024622", "72975978136470898183217648961745628914523492408810350" ]
Number of switching networks with C(2,n) acting on the domain and AG(3,2) acting on the domain.
A000885
[ "0", "2", "4", "6", "10", "12", "19", "21", "25", "33", "35", "46", "53", "56", "67", "80", "93", "98", "117", "128", "131", "146", "160", "174", "195", "210", "217", "227", "233", "244", "286", "298", "325", "331", "376", "386", "406", "423", "444", "467", "492", "505", "554", "561", "581", "589", "641", "700", "723", "732", "748", "780", "789", "835", "868", "895", "938", "945", "975" ]
Number of twin prime pairs < square of n-th prime.
A000886
[ "2", "11", "590", "7644658", "6406102803167154", "19692266672998575394929289976513119", "957275870017495002938079709038262383344122314736541166025242955633607263" ]
Number of switching networks with GL(n,2) acting on the domain and AG(2,2) acting on the range.
A000887
[ "2", "12", "2828", "8747130342", "491246345257275414284942", "6486753612131092188914472969769826152814897906580334" ]
Number of switching networks with GL(n,2) acting on the domain and AG(3,2) acting on the range.
A000888
[ "1", "2", "12", "100", "980", "10584", "121968", "1472328", "18404100", "236390440", "3103161776", "41469525552", "562496897872", "7726605740000", "107289439704000", "1503840313184400", "21252802073091300", "302539888334593800", "4334635827016110000", "62464383654579522000", "904841214653480504400" ]
a(n) = (2*n)!^2 / ((n+1)!*n!^3).
A000889
[ "2", "7", "124", "494298", "200221917406630", "307691667840351694566029898844575", "7478717734511679718967611872518416516838871889762225738677912465064319" ]
Number of switching networks with S(n) and C(2,2) acting on the domain and AG(2,2) acting on the range.
A000890
[ "2", "8", "502", "547849868", "15351457458188948591044", "101355525189553716762153010939347719113626111895054", "45444210218450590048352761382977278474163061892945988503535816179384800906003492121663432508203634748567436" ]
Number of switching networks with S(n) and C(2,2) acting on the domain and AG(2,3) acting on the range.
A000891
[ "1", "3", "20", "175", "1764", "19404", "226512", "2760615", "34763300", "449141836", "5924217936", "79483257308", "1081724803600", "14901311070000", "207426250094400", "2913690606794775", "41255439318353700", "588272005095043500" ]
a(n) = (2*n)!*(2*n+1)! / (n! * (n+1)!)^2.
A000892
[ "2", "7", "60", "13733", "77443340533", "703340569806668663530742581", "29445655130242047875797696478261941465296049517922025033117465" ]
Number of switching networks with GL(n,2) acting on the domain and AG(2,2) acting on the range.
A000893
[ "2", "8", "214", "10740500", "5895494078673763322", "231684599677799190148636584446502265460151192" ]
Number of switching networks with GL(n,2) acting on the domain and AG(3,2) acting on the range.
A000894
[ "1", "6", "60", "700", "8820", "116424", "1585584", "22084920", "312869700", "4491418360", "65166397296", "953799087696", "14062422446800", "208618354980000", "3111393751416000", "46619049708716400", "701342468412012900" ]
a(n) = (2*n)!*(2*n+1)! /((n+1)! *n!^3).
A000895
[ "2", "5", "24", "1430", "2440325272", "10989701416724479725189828", "230044180705016098807922033434683198117461325308508929710583" ]
Number of switching networks with AG(n,2) acting on the domain and AG(2,2) acting on the range.
A000896
[ "2", "6", "70", "700229", "184239362390740969", "3620071869990730348276861702715495626355546", "1397856755476623081643981198354119089406016417825924278115794483751825503676804770385912700712220" ]
Number of switching networks with AG(n,2) acting on the domain and AG(3,2) acting on the range.
A000897
[ "1", "12", "420", "18480", "900900", "46558512", "2498640144", "137680171200", "7735904619300", "441233078286000", "25467973278667920", "1484298740174927040", "87202550985276963600", "5157850293780050462400", "306839461354466267304000", "18344908596179023234548480" ]
a(n) = (4*n)! / ((2*n)!*n!^2).
A000898
[ "1", "2", "6", "20", "76", "312", "1384", "6512", "32400", "168992", "921184", "5222208", "30710464", "186753920", "1171979904", "7573069568", "50305536256", "342949298688", "2396286830080", "17138748412928", "125336396368896", "936222729254912", "7136574106003456", "55466948299223040", "439216305474605056", "3540846129311916032" ]
a(n) = 2*(a(n-1) + (n-1)*a(n-2)) for n >= 2 with a(0) = 1.
A000899
[ "0", "0", "0", "1", "9", "70", "571", "4820", "44676", "450824", "4980274", "59834748", "778230060", "10896609768", "163456629604", "2615335902176", "44460874280032", "800296440705472", "15205636325496568", "304112744618157872", "6386367741011250672" ]
Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
A000900
[ "0", "0", "0", "1", "2", "10", "28", "106", "344", "1272", "4592", "17692", "69384", "283560", "1191984", "5171512", "23087168", "105883456", "498572416", "2404766224", "11878871456", "59975885856", "309439708352", "1628919330208", "8746079933568", "47840206525056" ]
Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).