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A003738 Number of Hamiltonian paths in W_5 X P_n. 1
24, 1920, 70184, 2154592, 58772296, 2907860192, 155789578368, 8657124623872, 486468905555968, 27396295154262016, 1543844945278500864, 87013000712650358784, 4904346018649432653824, 276428194803652843536384, 15580616335530275077357568, 878187384790382283606458368, 49498247371236620586614521856 (list; graph; refs; listen; history; text; internal format)
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*(6720743*x^4 +216352*x^3 +5243*x^2 -60*x -3)/(56832*x^4 +3328*x^3 +128*x^2 -60*x +1). [Colin Barker, Aug 31 2012]

MATHEMATICA

CoefficientList[Series[-8 (6720743 x^4 + 216352 x^3 + 5243 x^2 - 60 x-3)/(56832 x^4 + 3328 x^3 + 128 x^2 - 60 x + 1), {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

CROSSREFS

Sequence in context: A123794 A269648 A269338 * A006685 A002671 A225220

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

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)