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Search: id:A102591
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| A102591 |
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a(n)=sum k=0..n, C(2n+1,2k)3^(n-k). |
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+0
3
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| 1, 6, 44, 328, 2448, 18272, 136384, 1017984, 7598336, 56714752, 423324672, 3159738368, 23584608256, 176037912576, 1313964867584, 9807567290368, 73204678852608, 546407161659392, 4078438577864704, 30441879976280064
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In general, sum{k=0..n, C(2n+1,2k)r^(n-k)} has g.f. (1-(r-1)x)/(1-2(r+1)+(r-1)^2x^2), and a(n)=((sqrt(r)-1)^(2n+1)+(sqrt(r)+1)^(2n+1))/(2sqrt(r)).
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FORMULA
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G.f.: (1-2x)/(1-8x+4x^2); a(n)=8a(n-1)-4a(n-2); a(n)=sqrt(3)(sqrt(3)-1)^(2n+1)/6+sqrt(3)(sqrt(3)+1)^(2n+1)/6.
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CROSSREFS
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Cf. A066443, A102592.
Sequence in context: A000561 A091162 A091163 this_sequence A114935 A115969 A082412
Adjacent sequences: A102588 A102589 A102590 this_sequence A102592 A102593 A102594
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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), Jan 22 2005
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