A003765 Number of Hamiltonian cycles in W_4 X P_n.

1, 10, 46, 238, 1170, 5882, 29278, 146382, 730434, 3647994, 18212046, 90936494, 454029874, 2266968122, 11318785790, 56514147406, 282171551586, 1408866513082, 7034386262766, 35122279177902

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

Table of n, a(n) for n=1..20.

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(1) = 1,

a(2) = 10,

a(3) = 46,

a(4) = 238,

a(5) = 1170,

a(6) = 5882 and

a(n) = 5a(n-1) + 3a(n-2) - 19a(n-3) + 20a(n-4) - 4a(n-5).

G.f.: x(1+5x-7x^2-3x^3+12x^4-4x^5)/(1-5x-3x^2+19x^3-20x^4+4x^5). [From R. J. Mathar, Dec 16 2008]

Crossrefs

Sequence in context: A183133 A115712 A199313 * A138041 A351901 A219597

Adjacent sequences: A003762 A003763 A003764 * A003766 A003767 A003768

Keyword

nonn

Author

Frans J. Faase

Extensions

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

Status

approved