A003736 Number of 2-factors in W_5 X P_n.

4, 156, 3832, 101476, 2653176, 69537644, 1821675752, 47726949876, 1250396334280, 32759217743932, 858260185404312, 22485600623006756, 589101327485494424, 15433894026086119116, 404353331486123621320, 10593672372980858817748, 277544131820420163065832, 7271392053421269671583068

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..700

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 (21,149,-285,-1354,1098,-24).

Formula

a(1) = 4,

a(2) = 156,

a(3) = 3832,

a(4) = 101476,

a(5) = 2653176,

a(6) = 69537644, and

a(n) = 21a(n-1) + 149a(n-2) - 285a(n-3) - 1354a(n-4) + 1098a(n-5) - 24a(n-6).

G.f.: -4*x*(x -1)*(6*x^4 -266*x^3 +9*x^2 +19*x +1)/(24*x^6 -1098*x^5 +1354*x^4 +285*x^3 -149*x^2 -21*x +1). - Colin Barker, Aug 30 2012

Mathematica

CoefficientList[Series[-4 (x - 1) (6 x^4 - 266 x^3 + 9 x^2 + 19 x + 1)/(24 x^6 - 1098 x^5 + 1354 x^4 + 285 x^3 - 149 x^2 - 21 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)

Prog

(Magma) I:=[4, 156, 3832, 101476, 2653176, 69537644]; [n le 6 select I[n] else 21*Self(n-1)+149*Self(n-2)-285*Self(n-3)-1354*Self(n-4)+1098*Self(n-5)-24*Self(n-6): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) Vec(-4*x*(x-1)*(6*x^4-266*x^3+9*x^2+19*x+1)/(24*x^6-1098*x^5+1354*x^4+285*x^3-149*x^2-21*x+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

Crossrefs

Sequence in context: A370230 A093977 A202298 * A354285 A210837 A289231

Adjacent sequences: A003733 A003734 A003735 * A003737 A003738 A003739

Keyword

nonn,easy

Author

Frans J. Faase

Extensions

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

More terms from Vincenzo Librandi, Oct 14 2013

Status

approved