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A100302 Expansion of (1-x-6x^2)/((1-x)(1-x-8x^2)). 3
1, 1, 3, 5, 23, 57, 235, 685, 2559, 8033, 28499, 92757, 320743, 1062793, 3628731, 12131069, 41160911, 138209457, 467496739, 1573172389, 5313146295, 17898525401, 60403695755, 203591898957, 686821464991, 2315556656641 (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 extremity nodes. a(n) counts closed walks of length n at each of the extremity nodes.

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)=(2^(-n)(sqrt(33)-1)^(n+1)(-1)^n+2^(-n)(sqrt(33)+1)^(n+1))sqrt(33)/264+3/4.

CROSSREFS

Cf. A015443, A100303.

Sequence in context: A148554 A120937 A075307 * A290384 A023247 A027753

Adjacent sequences:  A100299 A100300 A100301 * A100303 A100304 A100305

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 12 2004

STATUS

approved

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)