A145416 Number of Hamiltonian cycles in P_7 X P_2n.

1, 92, 5320, 301384, 17066492, 966656134, 54756073582, 3101696069920, 175698206778318, 9952578156814524, 563772503196695338, 31935387285412942410, 1809007988782552388490, 102472842263117124008066, 5804663918990466729365476, 328810272735298761062754308

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

Seiichi Manyama, Table of n, a(n) for n = 1..500

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

Recurrence:

a(1) = 1,

a(2) = 92,

a(3) = 5320,

a(4) = 301384,

a(5) = 17066492,

a(6) = 966656134,

a(7) = 54756073582,

a(8) = 3101696069920,

a(9) = 175698206778318,

a(10) = 9952578156814524,

a(11) = 563772503196695338,

a(12) = 31935387285412942410,

a(13) = 1809007988782552388490,

a(14) = 102472842263117124008066,

a(15) = 5804663918990466729365476,

a(16) = 328810272735298761062754308,

a(17) = 18625745945872429428768223714,

a(18) = 1055071695766249759732087999456, and

a(n) = 85a(n-1) - 1932a(n-2) + 20403a(n-3) - 116734a(n-4) + 386724a(n-5)

- 815141a(n-6) + 1251439a(n-7) - 1690670a(n-8) + 2681994a(n-9)

- 4008954a(n-10) + 3390877a(n-11) - 1036420a(n-12) - 178842a(n-13)

+ 92790a(n-14) + 17732a(n-15) - 5972a(n-16) + 1728a(n-17) + 144a(n-18).

Crossrefs

Cf. A321172.

Sequence in context: A035808 A017755 A157838 * A093292 A093246 A267787

Adjacent sequences: A145413 A145414 A145415 * A145417 A145418 A145419

Keyword

nonn

Author

N. J. A. Sloane, Feb 03 2009

Extensions

Recurrence corrected by Frans J. Faase, Feb 04 2009

Status

approved