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Search: id:A099622
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| A099622 |
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Sum C(n-k,k-1)4^(n-k-1)(5/4)^k, k=0..floor(n/2). |
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+0
2
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| 0, 1, 8, 53, 316, 1785, 9744, 51997, 273092, 1417889, 7299160, 37334661, 190028748, 963565513, 4871514656, 24572321645, 123720601684, 622038982257, 3123938806632, 15674669614549, 78593250398300, 393845861293721
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OFFSET
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0,3
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COMMENT
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In general a(n)=sum{k=0..floor(n/2),C(n-k,k+1)u^(n-k-1)(v/u)^(k-1)} has g.f. x^2/((1-u*x)(1-u*x-v*x^2)) and satisfies the recurrence a(n)=2u*a(n-1)-(u^2-v)a(n-2)-u*v*a(n-3).
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FORMULA
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G.f.: x^2/((1-4x)(1-4x-5x^2)); a(n)=8a(n-1)-11a(n-2)-20a(n-3).
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CROSSREFS
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Cf. A094705, A099621.
Adjacent sequences: A099619 A099620 A099621 this_sequence A099623 A099624 A099625
Sequence in context: A126503 A130153 A116171 this_sequence A110099 A091870 A054418
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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 25 2004
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