A003750 Number of Hamiltonian paths in K_5 X P_n.

60, 8760, 617400, 36021240, 1871009400, 90539967480, 4181860331640, 187073020183800, 8181829090755960, 352081040138505720, 14972983484769861240, 631272829225942738680, 26446059244840564688760, 1102721870861189212971000, 45821243162927769017364600

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..600

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 (95,-2854,23880,97152,29616,-19296,-6912).

Formula

a(1) = 60,

a(2) = 8760,

a(3) = 617400,

a(4) = 36021240,

a(5) = 1871009400,

a(6) = 90539967480,

a(7) = 4181860331640,

a(8) = 187073020183800, and

a(n) = 95a(n-1) - 2854a(n-2) + 23880a(n-3) + 97152a(n-4) + 29616a(n-5) - 19296a(n-6) - 6912a(n-7).

G.f.: 60*x*(6912*x^7 -48096*x^6 +39216*x^5 -66112*x^4 +15608*x^3 -726*x^2 +51*x +1)/((12*x^2 +28*x-1)^2*(48*x^3 -90*x^2 -39*x +1)). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[60 (6912 x^7 - 48096 x^6 + 39216 x^5 - 66112 x^4 + 15608 x^3 - 726 x^2 + 51 x + 1)/((12 x^2 + 28 x - 1)^2 (48 x^3 - 90 x^2 - 39 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(PARI) Vec(60*x*(6912*x^7-48096*x^6+39216*x^5-66112*x^4+15608*x^3-726*x^2+51*x+1)/((12*x^2+28*x-1)^2*(48*x^3-90*x^2-39*x+1))+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A130214 A295815 A146498 * A001525 A377667 A309996

Adjacent sequences: A003747 A003748 A003749 * A003751 A003752 A003753

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

Status

approved