A003766 Number of Hamiltonian paths in W_4 X P_n.

6, 152, 1608, 15420, 127980, 1003360, 7432708, 53294540, 371397240, 2537155684, 17047659916, 113102692016, 742597784164, 4835184613212, 31267479066856, 201066698078244, 1286998671857356, 8206523391863296

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

Table of n, a(n) for n=1..18.

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

Faase gives a 16-term linear recurrence on his web page:

a(1) = 6,

a(2) = 152,

a(3) = 1608,

a(4) = 15420,

a(5) = 127980,

a(6) = 1003360,

a(7) = 7432708,

a(8) = 53294540,

a(9) = 371397240,

a(10) = 2537155684,

a(11) = 17047659916,

a(12) = 113102692016,

a(13) = 742597784164,

a(14) = 4835184613212,

a(15) = 31267479066856,

a(16) = 201066698078244,

a(17) = 1286998671857356 and

a(n) = 14a(n-1) - 41a(n-2) - 193a(n-3) + 1025a(n-4) + 49a(n-5) - 5867a(n-6) + 7519a(n-7) + 6908a(n-8) - 23055a(n-9) + 16228a(n-10) + 2530a(n-11) - 7196a(n-12) + 832a(n-13) + 1568a(n-14) - 608a(n-15) + 64a(n-16).

Crossrefs

Sequence in context: A352757 A168654 A147796 * A278728 A221689 A354752

Adjacent sequences: A003763 A003764 A003765 * A003767 A003768 A003769

Keyword

nonn

Author

Frans J. Faase

Extensions

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

Status

approved