A003772 Number of Hamiltonian paths in K_4 X P_n.

12, 408, 6648, 90672, 1103088, 12509256, 135409896, 1419480288, 14545113696, 146607233784, 1460033574744, 14411647534224, 141321405768144, 1379055205227432, 13408489143753672, 130019327919243840, 1258252792162873152, 12158637295940721240

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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 (23,-173,421,62,-132,24).

Formula

Faase gives a 6-term linear recurrence on his web page:

a(1) = 12,

a(2) = 408,

a(3) = 6648,

a(4) = 90672,

a(5) = 1103088,

a(6) = 12509256,

a(7) = 135409896 and

a(n) = 23a(n-1) - 173a(n-2) + 421a(n-3) + 62a(n-4) - 132a(n-5) + 24a(n-6).

G.f.: 12*x*(24*x^6-164*x^5+398*x^4-275*x^3+55*x^2-11*x-1)/((2*x^2-7*x+1)^2*(6*x^2+9*x-1)). [Colin Barker, Aug 30 2012]

Mathematica

CoefficientList[Series[12(24 x^6 - 164 x^5 + 398 x^4 - 275 x^3 + 55 x^2 - 11 x - 1)/((2 x^2 - 7 x + 1)^2 (6 x^2 + 9 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{23, -173, 421, 62, -132, 24}, {12, 408, 6648, 90672, 1103088, 12509256, 135409896}, 20] (* Harvey P. Dale, Jun 11 2019 *)

Crossrefs

Sequence in context: A202788 A285028 A292784 * A211078 A299382 A197038

Adjacent sequences: A003769 A003770 A003771 * A003773 A003774 A003775

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

Status

approved