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A100305 Expansion of (1-x-4x^2)/(1-2x-7x^2+8x^3). 1
1, 1, 5, 9, 45, 113, 469, 1369, 5117, 16065, 56997, 185513, 641485, 2125585, 7257461, 24262137, 82321821, 276418913, 934993477, 3146344777, 10626292589, 35797050801, 120807391509, 407183797913, 1373642929981, 4631113313281 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Construct a graph as follows:form the graph whose adjacency matrix is the tensor product of that of P_3 and [1,1;1,1], then add a loop at each of the 'internal' nodes. (Spectrum : [0^3;1;(1-sqrt(33))/2;(1+sqrt(33))/2]). a(n) counts closed walks of length n at each of the 'internal' nodes. Partial sums of A100303.

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (2, 7, -8).

FORMULA

a(n)=2a(n-1)+7a(n-2)-8a(n-3); a(n)=1/2+((sqrt(33)+1)^(n+1)+(sqrt(33)-1)^(n+1)(-1)^n)sqrt(33)2^(-n)/132.

MATHEMATICA

CoefficientList[Series[(1-x-4x^2)/(1-2x-7x^2+8x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 7, -8}, {1, 1, 5}, 40] (* Harvey P. Dale, Oct 05 2012 *)

CROSSREFS

Cf. A100304.

Sequence in context: A149497 A149498 A149499 * A149500 A149501 A149502

Adjacent sequences:  A100302 A100303 A100304 * A100306 A100307 A100308

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 12 2004

STATUS

approved

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Last modified December 1 20:39 EST 2021. Contains 349435 sequences. (Running on oeis4.)