cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-13 of 13 results.

A145403 Number of nonintersecting rook paths joining opposite corners of 6 X n board.

Original entry on oeis.org

1, 32, 414, 5382, 79384, 1262816, 20562673, 336067810, 5493330332, 89803472792, 1468381290905, 24012936982592, 392716580997352, 6422777815120738, 105043595925333255, 1717976646746942760
Offset: 1

Views

Author

N. J. A. Sloane, Feb 03 2009

Keywords

Links

Crossrefs

Row 6 of A064298. Cf. A007764.

Formula

Recurrence:
a(1) = 1,
a(2) = 32,
a(3) = 414,
a(4) = 5382,
a(5) = 79384,
a(6) = 1262816,
a(7) = 20562673,
a(8) = 336067810,
a(9) = 5493330332,
a(10) = 89803472792,
a(11) = 1468381290905,
a(12) = 24012936982592,
a(13) = 392716580997352,
a(14) = 6422777815120738,
a(15) = 105043595925333255,
a(16) = 1717976646746942760,
a(17) = 28097347987645295129,
a(18) = 459529700981496318610,
a(19) = 7515570007661530339293,
a(20) = 122916531487036730334780,
a(21) = 2010289859051351461718841,
a(22) = 32878127252299185360551934,
a(23) = 537719101299048122399217869,
a(24) = 8794352250919537166665750722,
a(25) = 143830917261013287829855929053,
a(26) = 2352342978307852368872254574110,
a(27) = 38472378495706095194731534070125,
a(28) = 629212627935457125950913558054726,
a(29) = 10290721464101586255448326254366900,
a(30) = 168303914369885958800758915526318474,
a(31) = 2752596860300114955964065429361536989,
a(32) = 45018498254837163421818726088041699166,
a(33) = 736273885345044284085688553892457204990,
a(34) = 12041699640279371326340375422350041719446,
a(35) = 196941020336151050199143987475335247318191,
a(36) = 3220954404252653214796052011262240269847376,
a(37) = 52678447875240888447093955411712504021593807,
a(38) = 861551739720563513304275975426292082337631174,
a(39) = 14090608781288751611582325118090142798190478571,
a(40) = 230450763051941815978795941071686604125891198442,
a(41) = 3769003526784804976816338101329440702079133017666,
a(42) = 61641746795668086369885223391335280193549793452454,
a(43) = 1008145766120479656207584228935637479155797947389803,
a(44) = 16488142185777157345793212901099082094584264689337958,
a(45) = 269662227303264323330785234671779693565559562284410182,
a(46) = 4410303842290033896172439105038616399715156984924650402,
a(47) = 72130161409086529608951854829851816002712963801157839787,
a(48) = 1179682935903881340573479585181430128337758733576064749582,
a(49) = 19293618675966098340238272567572020098236154654850930308513,
a(50) = 315545567613362204775242670274937424600545170340425654393866,
a(51) = 5160722149260222882522006042304141173305206572051170726255899,
a(52) = 84403191917113277982043589954202883741227100622483260510931370,
a(53) = 1380407353807693358300087458031214954879276213089038340492802025,
a(54) = 22576450240384821778027453624243941724086228917427154372144432134,
a(55) = 369236011421291236034279467148078460540271871269615690271797866884,
a(56) = 6038825000328308509532140773346231121610228947574581160028281180694,
a(57) = 98764492781235197642079658639806209320318476451903082795917783012815,
a(58) = 1615285263905535856420093270568679674123758786480792514826877881411406,
a(59) = 26417859397806804999115463757296013189790610675906972739777532953432044,
a(60) = 432061946429732109168468779744829065082966074684439846926537350314283068,
a(61) = 7066338068562305854471591381542565889032938460560686542553098493028726504,
a(62) = 115569385621266871108822160868123881005301075723863358645704767187297221382,
a(63) = 1890127922452274019805513045202943498801049603564334398540115110078021072823,
a(64) = 30912888772650264652219507061031956074793682526018605864614278139682619190156,
a(65) = 505577787047572692090462300937222384232557420150184666960671714745016065033080,
a(66) = 8268683675466366377840360356400869587932159727058836866913105126545228412490614,
a(67) = 135233650442183190541354312834185782890515070868821995834750746327337159470828189,
a(68) = 2211735377685386523121420331929400511514963984542634134765620183963171569729235278,
a(69) = 36172752601960652644405183597210303325660884461711588396278289372424954431031849588,
a(70) = 591602433095763079343906237098879371053254029141187068993235175242965360620853115872,
a(71) = 9675609779993804523757669609814376179537455425273511736449480229116222799072745849896,
a(72) = 158243812698379899306192927052283225599988748265808627411791715806385192535377775606282,
a(73) = 2588064713926068829323899654190495449456281961482820545222829156707671713277546826822289,
a(74) = 42327588354029840959980586262134563828846542737714855516560279055906134220418117167021544,
a(75) = 692264272306516416237168808269386146006151827583985698688727056187756308291243240771646474, and
a(n) = 76a(n-1) - 2640a(n-2) + 55984a(n-3) - 812934a(n-4) + 8556872a(n-5)
- 67099242a(n-6) + 393958772a(n-7) - 1692942183a(n-8) + 4884527404a(n-9) - 6187506869a(n-10)
- 19086405626a(n-11) + 128174201130a(n-12) - 327127420664a(n-13) + 297315119122a(n-14) + 743733332720a(n-15)
- 3157843190533a(n-16) + 5268656094548a(n-17) - 3941342671128a(n-18) - 3509217289604a(n-19) + 25691997627302a(n-20)
- 79177609422932a(n-21) + 124810724415142a(n-22) + 32165552119276a(n-23) - 559590816744166a(n-24) + 954577325227640a(n-25)
+ 45695215480520a(n-26) - 2489003696662264a(n-27) + 3079811130140804a(n-28) + 1436343394106164a(n-29) - 6800600057977368a(n-30)
+ 3717237179493356a(n-31) + 6652945245605814a(n-32) - 9432540370407444a(n-33) - 2036411447626966a(n-34) + 12103828254803672a(n-35)
- 3892070556133820a(n-36) - 11936409494863372a(n-37) + 8331936811395842a(n-38) + 10790544774261660a(n-39) - 9791814381222907a(n-40)
- 9774483491028244a(n-41) + 8082925131170466a(n-42) + 8591527532922680a(n-43) - 4558074323604317a(n-44) - 6507699416893516a(n-45)
+ 1335741921421883a(n-46) + 3811541403121978a(n-47) + 265590026556815a(n-48) - 1596050169969560a(n-49) - 489317457105434a(n-50)
+ 441751378351184a(n-51) + 251839358248300a(n-52) - 69448285619300a(n-53) - 76332173161850a(n-54) + 1539583576296a(n-55)
+ 15557344027403a(n-56) + 2097787252080a(n-57) - 2266145094960a(n-58) - 598133889956a(n-59) + 240729252424a(n-60)
+ 98573852340a(n-61) - 17808243041a(n-62) - 11420445450a(n-63) + 718791367a(n-64) + 980442116a(n-65)
+ 34587845a(n-66) - 51217686a(n-67) - 4961985a(n-68) + 1519440a(n-69) + 196028a(n-70)
- 26928a(n-71) - 3486a(n-72) + 308a(n-73) + 25a(n-74) - 2a(n-75).

A333812 Number of self-avoiding paths joining opposite corners of 7 X n board.

Original entry on oeis.org

1, 64, 1369, 29739, 752061, 20562673, 575780564, 16230458696, 459133264944, 13021391001373, 369886375079581, 10516022622412960, 299104709252534435, 8509249843020438582, 242108399244641421526, 6888987223916209602814, 196026708756588099010848
Offset: 1

Views

Author

Seiichi Manyama, Apr 06 2020

Keywords

Links

Crossrefs

Row 7 of A064298.

Programs

  • Python
    # Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A064298(n, k):
    if n == 1 or k == 1: return 1
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    start, goal = 1, k * n
    paths = GraphSet.paths(start, goal)
    return paths.len()
def A333812(n):
    return A064298(n, 7)
print([A333812(n) for n in range(1, 20)])

A342936 Array T(n, k), n, k > 0, read by antidiagonals; T(n, k) is the number of rotationally symmetric self-avoiding rook paths joining opposite corners of an n X k board.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 0, 4, 0, 1, 1, 4, 6, 6, 4, 1, 1, 0, 13, 0, 13, 0, 1, 1, 8, 20, 34, 34, 20, 8, 1, 1, 0, 43, 0, 120, 0, 43, 0, 1, 1, 16, 66, 187, 320, 320, 187, 66, 16, 1, 1, 0, 142, 0, 1137, 0, 1137, 0, 142, 0, 1, 1, 32, 218, 1026, 3026, 5321, 5321, 3026, 1026, 218, 32, 1
Offset: 0

Views

Author

Rémy Sigrist, Apr 11 2021

Keywords

Examples

			Array T(n, k) begins:
  n\k|  1   2    3     4      5      6       7        8         9
  ---+-----------------------------------------------------------
    1|  1   1    1     1      1      1       1        1         1
    2|  1   0    2     0      4      0       8        0        16
    3|  1   2    4     6     13     20      43       66       142
    4|  1   0    6     0     34      0     187        0      1026
    5|  1   4   13    34    120    320    1137     3026     10725
    6|  1   0   20     0    320      0    5321        0     87298
    7|  1   8   43   187   1137   5321   32916   152606    939548
    8|  1   0   66     0   3026      0  152606        0   7592509
    9|  1  16  142  1026  10725  87298  939548  7592509  81253506

Links

Crossrefs

Cf. A064298.

Programs

  • C
    See Links section.

Formula

T(n, k) <= A064298(n, k).
T(n, k) = T(k, n).
T(n, k) = 0 iff n and k are both even.
T(n, 1) = 1.
T(2*k+1, 2) = 2^k for any k >= 0.
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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