A145405 Number of 2-factors in O_6 X P_n.

20, 2984, 340852, 40071100, 4696965476, 550730736140, 64572426811780, 7571054816109868, 887698562638519076, 104081767587749759756, 12203482981057263416260, 1430846154730977823707628, 167765278289617542860512868, 19670310820391775621430114508

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

Alois P. Heinz, Table of n, a(n) for n = 1..150

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 (113,585,-10329,17644,3148,-8496).

Formula

Recurrence:

a(1) = 20,

a(2) = 2984,

a(3) = 340852,

a(4) = 40071100,

a(5) = 4696965476,

a(6) = 550730736140, and

a(n) = 113a(n-1) + 585a(n-2) - 10329a(n-3) + 17644a(n-4) + 3148a(n-5) - 8496a(n-6).

G.f.: -4*x*(2124*x^5-403*x^4-3941*x^3+2010*x^2-181*x-5) / (8496*x^6 -3148*x^5 -17644*x^4 +10329*x^3 -585*x^2 -113*x+1). [Colin Barker, Aug 23 2012]

Maple

a:= n-> (Matrix (6, (i, j)-> `if` (i=j-1, 1, `if` (i=6, [-8496, 3148, 17644, -10329, 585, 113][j], 0)))^n. <<1, 20, 2984, 340852, 40071100, 4696965476>>) [1, 1]: seq (a(n), n=1..20);  # Alois P. Heinz, Aug 28, 2011

Crossrefs

Sequence in context: A222943 A222750 A250019 * A028458 A225989 A332265

Adjacent sequences: A145402 A145403 A145404 * A145406 A145407 A145408

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 03 2009

Status

approved