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Search: id:A100302
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| A100302 |
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Expansion of (1-x-6x^2)/((1-x)(1-x-8x^2)). |
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+0
4
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| 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; 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 extremity nodes. a(n) counts closed walks of length n at each of the extremity nodes.
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FORMULA
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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.
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CROSSREFS
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Cf. A015443, A100303.
Sequence in context: A065720 A120937 A075307 this_sequence A023247 A027753 A066411
Adjacent sequences: A100299 A100300 A100301 this_sequence A100303 A100304 A100305
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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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