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Search: id:A015440
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| A015440 |
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Generalized Fibonacci numbers. |
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+0
7
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| 1, 1, 6, 11, 41, 96, 301, 781, 2286, 6191, 17621, 48576, 136681, 379561, 1062966, 2960771, 8275601, 23079456, 64457461, 179854741, 502142046, 1401415751, 3912125981, 10919204736, 30479834641, 85075858321, 237475031526
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Joerg Arndt, Fxtbook
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FORMULA
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a(n) = a(n-1) + 5 a(n-2).
a(n)={[ (1+sqrt(21))/2 ]^(n+1) - [ (1-sqrt(21))/2 ]^(n+1)}/sqrt(21).
a(n)=sum(k=0, ceil(n/2), 5^k*binomial(n-k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004
G.f.: 1/(1-x-5x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2008]
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CROSSREFS
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Cf. A006130, A006131, A015441.
Adjacent sequences: A015437 A015438 A015439 this_sequence A015441 A015442 A015443
Sequence in context: A108698 A002570 A038265 this_sequence A094555 A099437 A077701
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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