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Search: id:A099912
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| A099912 |
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Number of closed walks on the Herschel graph. |
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+0
2
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| 1, 4, 32, 328, 3560, 39064, 429512, 4724248, 51965960, 571624024, 6287861192, 69166466968, 760831124360, 8369142343384, 92060565728072, 1012666222910488, 11139328451818760, 122532612969613144, 1347858742664958152
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Counts closed walks of length 2n at any node of degree 4 on the Herschel graph. With interpolated zeros, counts closed walks of length n. The g.f. is then (1-9x^2+2x^4)/((1-2x^2)(1-11x^2))=(1-14x^2+53x^4-64x^6+12x^8)/((1-2x^2)^2(1-3x^2)(1-11x^2)). Binomial transform of A099913.
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LINKS
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Eric Weisstein's World of Mathematics, Herschel Graph
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FORMULA
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G.f. : (1-9x+2x^2)/((1-2x)(1-11x)); a(n)=0^n/11+811^(n-1)/3+2^(n+1)/3.
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CROSSREFS
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Adjacent sequences: A099909 A099910 A099911 this_sequence A099913 A099914 A099915
Sequence in context: A052704 A090004 A061631 this_sequence A002005 A123309 A051489
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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), Oct 30 2004
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