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Search: id:A100304
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| A100304 |
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Expansion of (1-x-6x^2)/(1-x-8x^2). |
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+0
2
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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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.
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FORMULA
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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
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CROSSREFS
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Cf. A100305.
Adjacent sequences: A100301 A100302 A100303 this_sequence A100305 A100306 A100307
Sequence in context: A074970 A087338 A055735 this_sequence A096190 A136434 A001183
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 12 2004
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