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A160149 Number of Hamilton cycles in P_9 X P_2n. 3
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 Hamilton 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.

Index entries for sequences related to graphs, Hamiltonian

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: A249705 A197647 A238034 * A251224 A210384 A215195

Adjacent sequences:  A160146 A160147 A160148 * A160150 A160151 A160152

KEYWORD

nonn

AUTHOR

Artem M. Karavaev, May 03 2009

STATUS

approved

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Last modified April 25 10:11 EDT 2017. Contains 285379 sequences.