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A160149 Number of Hamiltonian cycles in P_9 X P_2n. 5
1, 596, 175294, 49483138, 13916993782, 3913787773536, 1100831164969864, 309656520296472068, 87106950271042689032, 24503579727182933530758, 6892987382635818948665404, 1939035566761570513740174424 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..104 . [From Robert G. Wilson v, May 20 2010]
Robert Stoyan and Volker Strehl, Enumeration of Hamiltonian Circuits in rectangular grids, Seminaire Lotharingien de Combinatoire, B34f (1995), 21pp.
FORMULA
Recurrence: a(n) = 672a(n-1)
- 178941a(n-2)
+ 26786039a(n-3)
- 2607448600a(n-4)
+ 179022506347a(n-5)
- 9138846694357a(n-6)
+ 360041299997972a(n-7)
- 11254854430370909a(n-8)
+ 285239012592685968a(n-9)
- 5964627217090541641a(n-10)
+ 104500678360781697484a(n-11)
- 1556583951761808187351a(n-12)
+ 20014735589628148063803a(n-13)
- 225840870982639685350870a(n-14)
+ 2275592733721786744418588a(n-15)
- 20826364708844211419088048a(n-16)
+ 175698356667789807902833571a(n-17)
- 1381174156518847754742200917a(n-18)
+ 10170019003804901336735147471a(n-19)
- 70003420053325632588023367766a(n-20)
+ 446182037050452191079109199615a(n-21)
- 2595362044476627757245437008109a(n-22)
+ 13570008625005415621556838250183a(n-23)
- 63003395189524492106909601816507a(n-24)
+ 257826103840415278692445505871098a(n-25)
- 927795089970952084248323277475301a(n-26)
+ 2943063243792739889950387942270474a(n-27)
- 8284388338421319713668314321950849a(n-28)
+ 20893786955948014423103382099606436a(n-29)
- 47682931456935989016644226476248441a(n-30)
+ 99034722216970869411718009120972998a(n-31)
- 186613940860788357047700590145469850a(n-32)
+ 314393511785306230125922905225687470a(n-33)
- 461228773076139092991049045910233189a(n-34)
+ 568163799314454613889626216489802291a(n-35)
- 569970237446092330623145821872270554a(n-36)
+ 516255441745874003918772527423187876a(n-37)
- 750331973988610457686979424425455695a(n-38)
+ 1948116315614897591684683097566788710a(n-39)
- 4767578165656000132898694536173303552a(n-40)
+ 9223068331940449503246199380170797588a(n-41)
- 14439385882606881084375341082872500069a(n-42)
+ 19203524833778237619399199496120112344a(n-43)
- 22654155027324560919450394582691204737a(n-44)
+ 24342554197365645052552314094292020138a(n-45)
- 24340773477750862776080869834954798051a(n-46)
+ 24250658103545708573796143054316829733a(n-47)
- 27745190966510447840996071368294727573a(n-48)
+ 38425792204525402615949097274689190884a(n-49)
- 55422759326895948871535222743427159802a(n-50)
+ 70729055476730900234366793432472266368a(n-51)
- 73819925880373004637572018001559769310a(n-52)
+ 63388514129546493372164181497486524518a(n-53)
- 52759270432980368768927960250795764010a(n-54)
+ 55764118845777226484391752561108715665a(n-55)
- 66464113509700746109349441075277770500a(n-56)
+ 62296605320562742399955687633954554900a(n-57)
- 31148391366039709828008192258625920077a(n-58)
- 12485250186916140101609953912898081887a(n-59)
+ 42654862914755984553959255801657245314a(n-60)
- 47023712901001741125118508732822852170a(n-61)
+ 33080927717174510775217853281082076598a(n-62)
- 15494466120988713368893421376058986544a(n-63)
+ 3429254057650617087578787175065609089a(n-64)
+ 1834366466922000360932519537787508153a(n-65)
- 2847750979275136270288226785862119971a(n-66)
+ 2216810876719448894152498968621570249a(n-67)
- 1347444141266719076559545050826163790a(n-68)
+ 701841127814802063228662479499782493a(n-69)
- 318066936221517953502258428878290012a(n-70)
+ 121105551713136925328282829822866983a(n-71)
- 34745081077056040606914781189637450a(n-72)
+ 4499432686690403495320601923345141a(n-73)
+ 2575385020956666440077901987225623a(n-74)
- 2619480426445702741842509277432650a(n-75)
+ 1531700770701230953980399995413110a(n-76)
- 725941992725792269897852489297623a(n-77)
+ 293308884467487194944446092523363a(n-78)
- 99272941541573765316896500953947a(n-79)
+ 26610547639802501699214550716520a(n-80)
- 4823713154410742640789125247946a(n-81)
+ 74930790097929859308142401662a(n-82)
+ 395529202546191570854138851376a(n-83)
- 214011709513320393200145896220a(n-84)
+ 78239618982805866166560174399a(n-85)
- 22992955661092007469888280252a(n-86)
+ 5643220564094431894769771279a(n-87)
- 1159808414772210919562895201a(n-88)
+ 197576217930011633432855397a(n-89)
- 27350727342373286714221107a(n-90)
+ 2950281377202644726344372a(n-91)
- 220666390717767574487088a(n-92)
+ 5787537137476979667629a(n-93)
+ 1229475105352798691453a(n-94)
- 232763105542097450138a(n-95)
+ 23427163147889339094a(n-96)
- 1633355302567880268a(n-97)
+ 82645890727987184a(n-98)
- 2982658741842664a(n-99)
+ 72036310273096a(n-100)
- 1019997566464a(n-101)
+ 5772791568a(n-102)
- 24126720a(n-103)
+ 628224a(n-104), with initial terms as given in the b-file.
CROSSREFS
Sequence in context: A321012 A238034 A293098 * A251224 A210384 A215195
KEYWORD
nonn
AUTHOR
Artem M. Karavaev, May 03 2009
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)