cp's OEIS Frontend

A160149 Number of Hamiltonian cycles in P_9 X P_2n.

%I A160149 #23 Jul 02 2025 01:01:21
%S A160149 1,596,175294,49483138,13916993782,3913787773536,1100831164969864,
%T A160149 309656520296472068,87106950271042689032,24503579727182933530758,
%U A160149 6892987382635818948665404,1939035566761570513740174424,545461572209610275803315881752,153441405974256213957573931981608
%N A160149 Number of Hamiltonian cycles in P_9 X P_2n.
%C A160149 Stoyan & Strehl determined the rational generating function for the number of Hamiltonian cycles in P_9 X P_n with degree of denominator equal to 208.
%H A160149 Huaide Cheng, <a href="/A160149/b160149.txt">Table of n, a(n) for n = 1..409</a> (terms 1..104 from Robert G. Wilson v)
%H A160149 Robert Stoyan and Volker Strehl, <a href="http://www.mat.univie.ac.at/~slc/wpapers/s34erlangen.html">Enumeration of Hamiltonian Circuits in rectangular grids</a>, Séminaire Lotharingien de Combinatoire, B34f (1995), 21pp.
%H A160149 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%H A160149 <a href="/index/Rec#order_104">Index entries for linear recurrences with constant coefficients</a>, order 104.
%F A160149 Recurrence: a(n) = 672a(n-1)
%F A160149 - 178941a(n-2)
%F A160149 + 26786039a(n-3)
%F A160149 - 2607448600a(n-4)
%F A160149 + 179022506347a(n-5)
%F A160149 - 9138846694357a(n-6)
%F A160149 + 360041299997972a(n-7)
%F A160149 - 11254854430370909a(n-8)
%F A160149 + 285239012592685968a(n-9)
%F A160149 - 5964627217090541641a(n-10)
%F A160149 + 104500678360781697484a(n-11)
%F A160149 - 1556583951761808187351a(n-12)
%F A160149 + 20014735589628148063803a(n-13)
%F A160149 - 225840870982639685350870a(n-14)
%F A160149 + 2275592733721786744418588a(n-15)
%F A160149 - 20826364708844211419088048a(n-16)
%F A160149 + 175698356667789807902833571a(n-17)
%F A160149 - 1381174156518847754742200917a(n-18)
%F A160149 + 10170019003804901336735147471a(n-19)
%F A160149 - 70003420053325632588023367766a(n-20)
%F A160149 + 446182037050452191079109199615a(n-21)
%F A160149 - 2595362044476627757245437008109a(n-22)
%F A160149 + 13570008625005415621556838250183a(n-23)
%F A160149 - 63003395189524492106909601816507a(n-24)
%F A160149 + 257826103840415278692445505871098a(n-25)
%F A160149 - 927795089970952084248323277475301a(n-26)
%F A160149 + 2943063243792739889950387942270474a(n-27)
%F A160149 - 8284388338421319713668314321950849a(n-28)
%F A160149 + 20893786955948014423103382099606436a(n-29)
%F A160149 - 47682931456935989016644226476248441a(n-30)
%F A160149 + 99034722216970869411718009120972998a(n-31)
%F A160149 - 186613940860788357047700590145469850a(n-32)
%F A160149 + 314393511785306230125922905225687470a(n-33)
%F A160149 - 461228773076139092991049045910233189a(n-34)
%F A160149 + 568163799314454613889626216489802291a(n-35)
%F A160149 - 569970237446092330623145821872270554a(n-36)
%F A160149 + 516255441745874003918772527423187876a(n-37)
%F A160149 - 750331973988610457686979424425455695a(n-38)
%F A160149 + 1948116315614897591684683097566788710a(n-39)
%F A160149 - 4767578165656000132898694536173303552a(n-40)
%F A160149 + 9223068331940449503246199380170797588a(n-41)
%F A160149 - 14439385882606881084375341082872500069a(n-42)
%F A160149 + 19203524833778237619399199496120112344a(n-43)
%F A160149 - 22654155027324560919450394582691204737a(n-44)
%F A160149 + 24342554197365645052552314094292020138a(n-45)
%F A160149 - 24340773477750862776080869834954798051a(n-46)
%F A160149 + 24250658103545708573796143054316829733a(n-47)
%F A160149 - 27745190966510447840996071368294727573a(n-48)
%F A160149 + 38425792204525402615949097274689190884a(n-49)
%F A160149 - 55422759326895948871535222743427159802a(n-50)
%F A160149 + 70729055476730900234366793432472266368a(n-51)
%F A160149 - 73819925880373004637572018001559769310a(n-52)
%F A160149 + 63388514129546493372164181497486524518a(n-53)
%F A160149 - 52759270432980368768927960250795764010a(n-54)
%F A160149 + 55764118845777226484391752561108715665a(n-55)
%F A160149 - 66464113509700746109349441075277770500a(n-56)
%F A160149 + 62296605320562742399955687633954554900a(n-57)
%F A160149 - 31148391366039709828008192258625920077a(n-58)
%F A160149 - 12485250186916140101609953912898081887a(n-59)
%F A160149 + 42654862914755984553959255801657245314a(n-60)
%F A160149 - 47023712901001741125118508732822852170a(n-61)
%F A160149 + 33080927717174510775217853281082076598a(n-62)
%F A160149 - 15494466120988713368893421376058986544a(n-63)
%F A160149 + 3429254057650617087578787175065609089a(n-64)
%F A160149 + 1834366466922000360932519537787508153a(n-65)
%F A160149 - 2847750979275136270288226785862119971a(n-66)
%F A160149 + 2216810876719448894152498968621570249a(n-67)
%F A160149 - 1347444141266719076559545050826163790a(n-68)
%F A160149 + 701841127814802063228662479499782493a(n-69)
%F A160149 - 318066936221517953502258428878290012a(n-70)
%F A160149 + 121105551713136925328282829822866983a(n-71)
%F A160149 - 34745081077056040606914781189637450a(n-72)
%F A160149 + 4499432686690403495320601923345141a(n-73)
%F A160149 + 2575385020956666440077901987225623a(n-74)
%F A160149 - 2619480426445702741842509277432650a(n-75)
%F A160149 + 1531700770701230953980399995413110a(n-76)
%F A160149 - 725941992725792269897852489297623a(n-77)
%F A160149 + 293308884467487194944446092523363a(n-78)
%F A160149 - 99272941541573765316896500953947a(n-79)
%F A160149 + 26610547639802501699214550716520a(n-80)
%F A160149 - 4823713154410742640789125247946a(n-81)
%F A160149 + 74930790097929859308142401662a(n-82)
%F A160149 + 395529202546191570854138851376a(n-83)
%F A160149 - 214011709513320393200145896220a(n-84)
%F A160149 + 78239618982805866166560174399a(n-85)
%F A160149 - 22992955661092007469888280252a(n-86)
%F A160149 + 5643220564094431894769771279a(n-87)
%F A160149 - 1159808414772210919562895201a(n-88)
%F A160149 + 197576217930011633432855397a(n-89)
%F A160149 - 27350727342373286714221107a(n-90)
%F A160149 + 2950281377202644726344372a(n-91)
%F A160149 - 220666390717767574487088a(n-92)
%F A160149 + 5787537137476979667629a(n-93)
%F A160149 + 1229475105352798691453a(n-94)
%F A160149 - 232763105542097450138a(n-95)
%F A160149 + 23427163147889339094a(n-96)
%F A160149 - 1633355302567880268a(n-97)
%F A160149 + 82645890727987184a(n-98)
%F A160149 - 2982658741842664a(n-99)
%F A160149 + 72036310273096a(n-100)
%F A160149 - 1019997566464a(n-101)
%F A160149 + 5772791568a(n-102)
%F A160149 - 24126720a(n-103)
%F A160149 + 628224a(n-104), with initial terms as given in the b-file.
%K A160149 nonn
%O A160149 1,2
%A A160149 _Artem M. Karavaev_, May 03 2009