A145407 Number of Hamiltonian paths in O_6 X P_n.

120, 41280, 6641952, 886927344, 105209243232, 16691618745408, 3453770804410752, 830385563124340992, 212352384742765204992, 55504372130542230537216, 14614230909478166949599232

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..11.

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 (350,-22608,-17280,843264).

Formula

Recurrence:

a(1) = 120,

a(2) = 41280,

a(3) = 6641952,

a(4) = 886927344,

a(5) = 105209243232, and

a(n) = 350a(n-1) - 22608a(n-2) - 17280a(n-3) + 843264a(n-4).

G.f.: 24*x*(2268414568*x^4 +20934334*x^3 +212212*x^2 +30*x -5)/((6*x -1)*(140544*x^3 +20544*x^2 -344*x +1)). [Colin Barker, Aug 31 2012]

Maple

A145407 := proc(n) option remember; if n <= 5 then op(n, [120, 41280, 6641952, 886927344, 105209243232]) ; else 350*procname(n-1)- 22608*procname(n-2) - 17280*procname(n-3) + 843264*procname(n-4); fi; end: seq(A145407(n), n=1..20) ; # R. J. Mathar, Mar 14 2009

Mathematica

Join[{120}, LinearRecurrence[{350, -22608, -17280, 843264}, {41280, 6641952, 886927344, 105209243232}, 10]] (* Jean-François Alcover, Apr 04 2020 *)

Crossrefs

Sequence in context: A054778 A230729 A027493 * A010798 A283829 A275457

Adjacent sequences: A145404 A145405 A145406 * A145408 A145409 A145410

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 03 2009

Extensions

More terms from R. J. Mathar, Mar 14 2009

Status

approved