A145412 Number of Hamiltonian paths in K_6 X P_n.

360, 275040, 102430080, 31321626480, 8516117133360, 2155827631204800, 520736224355831520, 121804259414668451280, 27852572730572966535120, 6266130842526092431103520, 1393142931205269478232279040, 307064506928289179560841957040, 67250721492106648169188058371440

Offset

1,1

References

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Links

Andrew Howroyd and Colin Barker, Table of n, a(n) for n = 1..427 (first 30 terms from Andrew Howroyd)

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs.

F. Faase, Results from the counting program

Index entries for linear recurrences with constant coefficients, signature (493,-76229,3141623,83807874,375481728,-11713248,-1292308992,1074456576,-238878720).

Formula

Recurrence:

a(1) = 360,

a(2) = 275040,

a(3) = 102430080,

a(4) = 31321626480,

a(5) = 8516117133360,

a(6) = 2155827631204800,

a(7) = 520736224355831520,

a(8) = 121804259414668451280,

a(9) = 27852572730572966535120,

a(10) = 6266130842526092431103520, and

a(n) = 493*a(n-1) - 76229*a(n-2) + 3141623*a(n-3) + 83807874*a(n-4) + 375481728*a(n-5) - 11713248*a(n-6) - 1292308992*a(n-7) + 1074456576*a(n-8) - 238878720*a(n-9).

G.f.: 360*x*(1 +271*x -15895*x^2 +1829547*x^3 -32069382*x^4 +43786376*x^5 -451478784*x^6 -35025408*x^7 +155602944*x^8 -39813120*x^9) / ((1 -145*x -516*x^2 +288*x^3)^2*(1 -203*x -2634*x^2 +2880*x^3)). - Colin Barker, Dec 22 2015

Prog

(PARI) Vec(360*x*(1 +271*x -15895*x^2 +1829547*x^3 -32069382*x^4 +43786376*x^5 -451478784*x^6 -35025408*x^7 +155602944*x^8 -39813120*x^9) / ((1 -145*x -516*x^2 +288*x^3)^2*(1 -203*x -2634*x^2 +2880*x^3)) + O(x^20)) \\ Colin Barker, Dec 22 2015

Crossrefs

Sequence in context: A200210 A263509 A317796 * A156032 A295452 A330906

Adjacent sequences: A145409 A145410 A145411 * A145413 A145414 A145415

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 03 2009

Extensions

a(11)-a(12) from Andrew Howroyd, Dec 21 2015

a(13) from Vincenzo Librandi, Dec 22 2015

Status

approved