A145400 Number of 2-factors in P_6 X P_n.

0, 5, 9, 222, 1140, 13903, 99051, 972080, 7826275, 71053230, 599141127, 5285091303, 45349095730, 395755191515, 3418116104881, 29709767180643, 257232791130155, 2232466696767889, 19346930092499853, 167813061128260612, 1454798219804865516, 12616086588695738786

Offset

1,2

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, Table of n, a(n) for n = 1..200

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

Formula

a(n) = 5*a(n-1) + 49*a(n-2) - 116*a(n-3) - 363*a(n-4) + 627*a(n-5) + 544*a(n-6) - 1061*a(n-7) + 133*a(n-8) + 264*a(n-9) - 47*a(n-10) - 26*a(n-11) + 3*a(n-12) + a(n-13) for n > 13.

G.f.: x^2*(5 - 16*x - 68*x^2 + 169*x^3 + 184*x^4 - 440*x^5 + 41*x^6 + 159*x^7 - 24*x^8 - 21*x^9 + 2*x^10 + x^11)/(1 - 5*x - 49*x^2 + 116*x^3 + 363*x^4 - 627*x^5 - 544*x^6 + 1061*x^7 - 133*x^8 - 264*x^9 + 47*x^10 + 26*x^11 - 3*x^12 - x^13). - Andrew Howroyd, Oct 04 2017

Crossrefs

Cf. A003693, A222202.

Sequence in context: A222374 A097397 A092584 * A002657 A046093 A097086

Adjacent sequences: A145397 A145398 A145399 * A145401 A145402 A145403

Keyword

nonn

Author

N. J. A. Sloane, Feb 03 2009

Extensions

Terms a(14) and beyond from Andrew Howroyd, Oct 04 2017

Status

approved