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Search: id:A101501
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| A101501 |
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Number of walks between adjacent nodes on C_5 tensor J_2. |
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+0
2
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| 0, 1, 0, 12, 8, 160, 224, 2240, 4608, 32512, 84480, 485376, 1464320, 7401472, 24608768, 114606080, 406093824, 1793720320, 6626869248, 28280881152, 107384668160, 448110002176, 1732341923840, 7123849183232, 27866041417728
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Let (C_5 tensor J_2) be the 10 node graph whose adjacency matrix is the tensor product of that of C_5 and J_2=[1,1;1,1]. Then a(n) counts walks of length n between adjacent vertices of this graph.
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REFERENCES
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E.R. van Dam, Graphs with few eigenvalues, Tilburg, 1968, p53.
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FORMULA
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G.f.: x(1-2x)/((1-4x)(1+2x-4x^2)); a(n)=2a(n-1)+12a(n-2)-16a(n-3); a(n)=(sqrt(5)-1)^(n+1)/20-(sqrt(5)+1)^(n+1)(-1)^n/20+4^n/10; a(n)=sum{k=0..n, sqrt(5)((sqrt(5)-1)^k/10-(-sqrt(5)-1)^k/10)(4^(n-k)+0^(n-k))/2}.
(1/10) [4^n - (-2)^n*Lucas(n+1) ]. - Ralf Stephan, May 16 2007
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CROSSREFS
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Cf. A101502.
Sequence in context: A040134 A121961 A038334 this_sequence A018870 A068614 A038335
Adjacent sequences: A101498 A101499 A101500 this_sequence A101502 A101503 A101504
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KEYWORD
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nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Dec 04 2004
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