1,2

Number of 2-factors in K_3 X P_n.

Form the graph with matrix [1,1,1,1;1,1,1,0;1,1,0,1;1,0,1,1]. The sequence 1,1,4,13... with g.f. (1-2x)/(1-3x-x^2) counts closed walks of length n at the vertex of degree 5. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004

a(n) = term (1,1) in M^n, M = the 3x3 matrix [1,1,2; 1,1,1; 1,1,1]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 12 2009]

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Index entries for sequences related to linear recurrences with constant coefficients

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 Hamilton cycles in product graphs

F. Faase, Results from the counting program

Joerg Arndt, Fxtbook

F. Faase, Counting Hamilton cycles in product graphs

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 419

Tanya Khovanova, Recursive Sequences

a(n)=(1/2-sqrt(13)/26)(3/2+sqrt(13)/2)^n+(1/2+sqrt(13)/26)(3/2-sqrt(13)/2)^n - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004

a(n)=Sum_{k, 0<=k<=n}2^k*A055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006

Starting (1, 1, 4, 13, 43, 142, 469,...), = row sums (unsigned) of triangle A136159. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 16 2007

G.f.: x*(1+x)/(1-3*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]

with(combinat): a:=n->fibonacci(n, 3)-2*fibonacci(n-1, 3): seq(a(n), n=2..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008

a[n_] := (MatrixPower[{{1, 3}, {1, 2}}, n].{{1}, {1}})[[1, 1]]; Table[ a[n], {n, 0, 23}] (from Robert G. Wilson v Jan 13 2005)

Partial sums of A052906. Pairwise sums of A006190.

Cf. A136159.

Sequence in context: A047144 A072307 A121486 this_sequence A033434 A113986 A149426

Adjacent sequences: A003685 A003686 A003687 this_sequence A003689 A003690 A003691

nonn

Frans Faase (Frans_LiXia(AT)wxs.nl)

Formula added Aug 15 1997 by Olivier Gerard