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Search: id:A099432
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| A099432 |
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Convolution of A030195(n) (generalized (3,3)-Fibonacci) with itself. |
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+0
1
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| 1, 6, 33, 162, 756, 3402, 14931, 64314, 273051, 1145988, 4764744, 19656756, 80561061, 328316814, 1331513397, 5377120038, 21633427836, 86747114430, 346810621815, 1382826606210, 5500378861551, 21830478128136, 86469557676048
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: 1/(1-3x-3x^2)^2; a(n)=6a(n-1)+3a(n-2)+18a(n-3)+9a(n-4); a(n)=sum{k=0..floor((n+2)/2), k*binomial(n-k+2, k)3^(n-k+1)}; a(n)=(sqrt(7)n+2sqrt(7)-sqrt(3))(5sqrt(7)/98+sqrt(3)/14)(3sqrt(21)/2 + 15/2)^(n/2) +(15/2-3sqrt(21)/2)^(n/2)(sqrt(7)n+2sqrt(7)+sqrt(3))(5sqrt(7)/98-sqrt(3)/14)(-1)^n.
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EXAMPLE
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sage: taylor( mul(x/(1 - 3*x - 3*x^2)^2 for i in xrange(1,2)),x,0,23)# solution >>x + 6*x^2 + 33*x^3 + 162*x^4 + 756*x^5 +....+ 5500378861551*x^21 + 21830478128136*x^22 + 86469557676048*x^23 + etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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PROGRAM
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(Other) sage: taylor( mul(x/(1 - 3*x - 3*x^2)^2 for i in xrange(1, 2)), x, 0, 23)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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CROSSREFS
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Cf. A073388.
Sequence in context: A120009 A074087 A022730 this_sequence A072260 A084153 A086314
Adjacent sequences: A099429 A099430 A099431 this_sequence A099433 A099434 A099435
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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 15 2004
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