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A145403 Number of nonintersecting rook paths joining opposite corners of 6 X n board. 2
1, 32, 414, 5382, 79384, 1262816, 20562673, 336067810, 5493330332, 89803472792, 1468381290905, 24012936982592, 392716580997352, 6422777815120738, 105043595925333255, 1717976646746942760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

F. Faase, Counting Hamiltonian cycles in product graphs.

F. Faase, Results from the counting program

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).

CROSSREFS

Row 6 of A064298. Cf. A007764.

Sequence in context: A195191 A275232 A061594 * A125116 A145217 A125444

Adjacent sequences:  A145400 A145401 A145402 * A145404 A145405 A145406

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 03 2009

STATUS

approved

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Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)