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Search: id:A003688
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| A003688 |
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a(n) = 3*a(n-1) + a(n-2). |
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+0
6
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| 1, 4, 13, 43, 142, 469, 1549, 5116, 16897, 55807, 184318, 608761, 2010601, 6640564, 21932293, 72437443, 239244622, 790171309, 2609758549, 8619446956, 28468099417, 94023745207, 310539335038, 1025641750321
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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LINKS
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Joerg Arndt, Fxtbook
Tanya Khovanova, Recursive Sequences
F. Faase, Counting Hamilton cycles in product graphs
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 419
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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)
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CROSSREFS
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Partial sums of A052906. Pairwise sums of A006190.
Cf. A136159.
Adjacent sequences: A003685 A003686 A003687 this_sequence A003689 A003690 A003691
Sequence in context: A047144 A072307 A121486 this_sequence A033434 A113986 A042767
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KEYWORD
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nonn
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AUTHOR
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Frans Faase (Frans_LiXia(AT)wxs.nl)
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EXTENSIONS
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Formula added Aug 15 1997 by Olivier Gerard
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