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A160149 Number of Hamiltonian cycles in P_9 X P_2n. 5

%I #13 Jan 01 2019 06:31:05

%S 1,596,175294,49483138,13916993782,3913787773536,1100831164969864,

%T 309656520296472068,87106950271042689032,24503579727182933530758,

%U 6892987382635818948665404,1939035566761570513740174424

%N Number of Hamiltonian cycles in P_9 X P_2n.

%C 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 Robert G. Wilson v, <a href="/A160149/b160149.txt">Table of n, a(n) for n = 1..104 </a>. [From _Robert G. Wilson v_, May 20 2010]

%H 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>, Seminaire Lotharingien de Combinatoire, B34f (1995), 21pp.

%H <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>

%F Recurrence: a(n) = 672a(n-1)

%F - 178941a(n-2)

%F + 26786039a(n-3)

%F - 2607448600a(n-4)

%F + 179022506347a(n-5)

%F - 9138846694357a(n-6)

%F + 360041299997972a(n-7)

%F - 11254854430370909a(n-8)

%F + 285239012592685968a(n-9)

%F - 5964627217090541641a(n-10)

%F + 104500678360781697484a(n-11)

%F - 1556583951761808187351a(n-12)

%F + 20014735589628148063803a(n-13)

%F - 225840870982639685350870a(n-14)

%F + 2275592733721786744418588a(n-15)

%F - 20826364708844211419088048a(n-16)

%F + 175698356667789807902833571a(n-17)

%F - 1381174156518847754742200917a(n-18)

%F + 10170019003804901336735147471a(n-19)

%F - 70003420053325632588023367766a(n-20)

%F + 446182037050452191079109199615a(n-21)

%F - 2595362044476627757245437008109a(n-22)

%F + 13570008625005415621556838250183a(n-23)

%F - 63003395189524492106909601816507a(n-24)

%F + 257826103840415278692445505871098a(n-25)

%F - 927795089970952084248323277475301a(n-26)

%F + 2943063243792739889950387942270474a(n-27)

%F - 8284388338421319713668314321950849a(n-28)

%F + 20893786955948014423103382099606436a(n-29)

%F - 47682931456935989016644226476248441a(n-30)

%F + 99034722216970869411718009120972998a(n-31)

%F - 186613940860788357047700590145469850a(n-32)

%F + 314393511785306230125922905225687470a(n-33)

%F - 461228773076139092991049045910233189a(n-34)

%F + 568163799314454613889626216489802291a(n-35)

%F - 569970237446092330623145821872270554a(n-36)

%F + 516255441745874003918772527423187876a(n-37)

%F - 750331973988610457686979424425455695a(n-38)

%F + 1948116315614897591684683097566788710a(n-39)

%F - 4767578165656000132898694536173303552a(n-40)

%F + 9223068331940449503246199380170797588a(n-41)

%F - 14439385882606881084375341082872500069a(n-42)

%F + 19203524833778237619399199496120112344a(n-43)

%F - 22654155027324560919450394582691204737a(n-44)

%F + 24342554197365645052552314094292020138a(n-45)

%F - 24340773477750862776080869834954798051a(n-46)

%F + 24250658103545708573796143054316829733a(n-47)

%F - 27745190966510447840996071368294727573a(n-48)

%F + 38425792204525402615949097274689190884a(n-49)

%F - 55422759326895948871535222743427159802a(n-50)

%F + 70729055476730900234366793432472266368a(n-51)

%F - 73819925880373004637572018001559769310a(n-52)

%F + 63388514129546493372164181497486524518a(n-53)

%F - 52759270432980368768927960250795764010a(n-54)

%F + 55764118845777226484391752561108715665a(n-55)

%F - 66464113509700746109349441075277770500a(n-56)

%F + 62296605320562742399955687633954554900a(n-57)

%F - 31148391366039709828008192258625920077a(n-58)

%F - 12485250186916140101609953912898081887a(n-59)

%F + 42654862914755984553959255801657245314a(n-60)

%F - 47023712901001741125118508732822852170a(n-61)

%F + 33080927717174510775217853281082076598a(n-62)

%F - 15494466120988713368893421376058986544a(n-63)

%F + 3429254057650617087578787175065609089a(n-64)

%F + 1834366466922000360932519537787508153a(n-65)

%F - 2847750979275136270288226785862119971a(n-66)

%F + 2216810876719448894152498968621570249a(n-67)

%F - 1347444141266719076559545050826163790a(n-68)

%F + 701841127814802063228662479499782493a(n-69)

%F - 318066936221517953502258428878290012a(n-70)

%F + 121105551713136925328282829822866983a(n-71)

%F - 34745081077056040606914781189637450a(n-72)

%F + 4499432686690403495320601923345141a(n-73)

%F + 2575385020956666440077901987225623a(n-74)

%F - 2619480426445702741842509277432650a(n-75)

%F + 1531700770701230953980399995413110a(n-76)

%F - 725941992725792269897852489297623a(n-77)

%F + 293308884467487194944446092523363a(n-78)

%F - 99272941541573765316896500953947a(n-79)

%F + 26610547639802501699214550716520a(n-80)

%F - 4823713154410742640789125247946a(n-81)

%F + 74930790097929859308142401662a(n-82)

%F + 395529202546191570854138851376a(n-83)

%F - 214011709513320393200145896220a(n-84)

%F + 78239618982805866166560174399a(n-85)

%F - 22992955661092007469888280252a(n-86)

%F + 5643220564094431894769771279a(n-87)

%F - 1159808414772210919562895201a(n-88)

%F + 197576217930011633432855397a(n-89)

%F - 27350727342373286714221107a(n-90)

%F + 2950281377202644726344372a(n-91)

%F - 220666390717767574487088a(n-92)

%F + 5787537137476979667629a(n-93)

%F + 1229475105352798691453a(n-94)

%F - 232763105542097450138a(n-95)

%F + 23427163147889339094a(n-96)

%F - 1633355302567880268a(n-97)

%F + 82645890727987184a(n-98)

%F - 2982658741842664a(n-99)

%F + 72036310273096a(n-100)

%F - 1019997566464a(n-101)

%F + 5772791568a(n-102)

%F - 24126720a(n-103)

%F + 628224a(n-104), with initial terms as given in the b-file.

%K nonn

%O 1,2

%A _Artem M. Karavaev_, May 03 2009

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)