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Search: id:A098525
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| A098525 |
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Expansion of (1+3x^2)/(1-x-9x^5). |
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+0
1
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| 1, 1, 4, 4, 4, 13, 22, 58, 94, 130, 247, 445, 967, 1813, 2983, 5206, 9211, 17914, 34231, 61078, 107932, 190831, 352057, 660136, 1209838, 2181226, 3898705, 7067218, 13008442, 23896984, 43528018, 78616363, 142221325, 259297303, 474370159
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The expansion of (1+kx^2)/(1-x-k^2*x^5) satisfies the recurrence a(n)=a(n-1)+k^2*a(n-5),a(0)=1,a(1)=1,a(2)=k+1,a(3)=k+1,a(4)=k+1, with a(n)=sum{k=0..floor(n/2), binomial(n-2k,floor(k/2))r^k}.
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FORMULA
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a(n)=a(n-1)+9a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))3^k}.
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CROSSREFS
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Sequence in context: A117405 A013601 A035618 this_sequence A102127 A131946 A034896
Adjacent sequences: A098522 A098523 A098524 this_sequence A098526 A098527 A098528
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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), Sep 12 2004
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