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A100304 Expansion of (1-x-6x^2)/(1-x-8x^2). 1
1, 0, 2, 2, 18, 34, 178, 450, 1874, 5474, 20466, 64258, 227986, 742050, 2565938, 8502338, 29029842, 97048546, 329287282, 1105675650, 3739973906, 12585379106, 42505170354, 143188203202, 483229566034, 1628735191650, 5494571719922 (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 extremity nodes. Partial sums are A100302.

LINKS

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1,8)

FORMULA

a(n)=3*0^n/4+(1/8-sqrt(33)/264)(1/2+sqrt(33)/2)^n+(1/8+sqrt(33)/264)(1/2-sqrt(33)/2)^n

CROSSREFS

Essentially half A100303. Cf. A100305.

Sequence in context: A055735 A168296 A205454 * A213271 A096190 A136434

Adjacent sequences:  A100301 A100302 A100303 * A100305 A100306 A100307

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 12 2004

STATUS

approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)