A003752 Number of Hamiltonian paths in C_4 X P_n.

4, 72, 584, 4016, 24656, 140624, 761960, 3976704, 20173280, 100097008, 488003448, 2345542720, 11142878992, 52426883056, 244682331976, 1134222633280, 5227498311360, 23975219772016, 109500177006104, 498322800625728, 2260840364623472, 10230065398683632

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 (11,-36,16,67,-9,-10,2).

Formula

a(1) = 4,

a(2) = 72,

a(3) = 584,

a(4) = 4016,

a(5) = 24656,

a(6) = 140624,

a(7) = 761960,

a(8) = 3976704 and

a(n) = 11a(n-1) - 36a(n-2) + 16a(n-3) + 67a(n-4) - 9a(n-5) - 10a(n-6) + 2a(n-7).

G.f.: -4*x*(2*x^7 +4*x^6 -37*x^5 +21*x^4 +30*x^3 -16*x^2 +7*x +1)/((x +1)*(x^2 -4*x +1)^2*(2*x^2 +4*x -1)). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[-4 (2 x^7 + 4 x^6 - 37 x^5 + 21 x^4 + 30 x^3 - 16 x^2 + 7 x + 1)/((x + 1) (x^2 - 4 x + 1)^2 (2 x^2 + 4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{11, -36, 16, 67, -9, -10, 2}, {4, 72, 584, 4016, 24656, 140624, 761960, 3976704}, 30] (* Harvey P. Dale, May 04 2018 *)

Prog

(Magma) I:=[4, 72, 584, 4016, 24656, 140624, 761960, 3976704]; [n le 8 select I[n] else 11*Self(n-1)-36*Self(n-2)+16*Self(n-3)+67*Self(n-4)-9*Self(n-5)-10*Self(n-6)+2*Self(n-7): n in [1..30]]; // Vincenzo Librandi, Oct 14 2013

Crossrefs

Sequence in context: A071683 A192826 A190398 * A062018 A192830 A119580

Adjacent sequences: A003749 A003750 A003751 * A003753 A003754 A003755

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

Status

approved