A003738 Number of Hamiltonian paths in W_5 X P_n.

24, 1920, 70184, 2154592, 58772296, 2907860192, 155789578368, 8657124623872, 486468905555968, 27396295154262016, 1543844945278500864, 87013000712650358784, 4904346018649432653824, 276428194803652843536384, 15580616335530275077357568, 878187384790382283606458368, 49498247371236620586614521856

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..580

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 (60,-128,-3328,-56832).

Formula

a(1) = 24, a(2) = 1920, a(3) = 70184, a(4) = 2154592, a(5) = 58772296, and a(n) = 60*a(n-1) - 128*a(n-2) - 3328*a(n-3) - 56832*a(n-4).

G.f.: 8*x*(3 +60*x -5243*x^2 -216352*x^3 -6720743*x^4)/(1 -60*x +128*x^2 +3328*x^3 +56832*x^4). - Colin Barker, Aug 31 2012

Maple

seq(coeff(series(8*x*(3 +60*x -5243*x^2 -216352*x^3 -6720743*x^4)/(1 -60*x +128*x^2 +3328*x^3 +56832*x^4), x, n+1), x, n), n = 1..40); # G. C. Greubel, Dec 25 2019

Mathematica

CoefficientList[Series[8*(3 +60*x -5243*x^2 -216352*x^3 -6720743*x^4)/(1 -60*x +128*x^2 +3328*x^3 +56832*x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(PARI) a(n) = if(n<1, 0, if(n<6, [24, 1920, 70184, 2154592, 58772296][n], 60*a(n-1) - 128*a(n-2) - 3328*a(n-3) - 56832*a(n-4) )); /* Joerg Arndt and Michael Somos, Aug 30 2012 */
(Magma) I:=[24, 1920, 70184, 2154592, 58772296]; [n le 5 select I[n] else 60*Self(n-1)-128*Self(n-2)-3328*Self(n-3)-56832*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(Sage)
def A003738_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 8*x*(3 +60*x -5243*x^2 -216352*x^3 -6720743*x^4)/(1 -60*x +128*x^2 +3328*x^3 +56832*x^4) ).list()
a=A003738_list(40); a[1:] # G. C. Greubel, Dec 25 2019
(GAP) a:=[1920, 70184, 2154592, 58772296];; for n in [5..40] do a[n]:=60*a[n-1] -128*a[n-2]-3328*a[n-3]-56832*a[n-4]; od; Concatenation([24], a); # G. C. Greubel, Dec 25 2019

Crossrefs

Sequence in context: A123794 A269648 A269338 * A006685 A002671 A328126

Adjacent sequences: A003735 A003736 A003737 * A003739 A003740 A003741

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

Terms corrected by Colin Barker, Aug 30 2012

Status

approved