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Search: id:A014334
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| A014334 |
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Exponential convolution of Fibonacci numbers with themselves. |
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+0
6
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| 0, 0, 2, 6, 22, 70, 230, 742, 2406, 7782, 25190, 81510, 263782, 853606, 2762342, 8939110, 28927590, 93611622, 302933606, 980313702, 3172361830, 10265978470, 33221404262, 107506722406, 347899061862
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(0)=0, a(1)=0, a(2)=2, a(n)=3a(n-1)+2a(n-2)-4a(n-3); n>0, a(n)=sum(k=0, n-1, 2^k*F(k)) where F(k) is the k-th Fibonacci number; a(n)=-2/5+((1+sqrt(5))^n+(1-sqrt(5))^n)/5 - Benoit Cloitre (benoit7848c(AT)orange.fr), May 29 2003
a(n)=sum(k=0, n, F(k)*F(n-k)*binomial(n, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 11 2005
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sum(k=0, n-1, fibonacci(k)*2^k))
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CROSSREFS
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Cf. A000045.
Cf. A103435.
Sequence in context: A126171 A002839 A109194 this_sequence A107239 A148496 A106434
Adjacent sequences: A014331 A014332 A014333 this_sequence A014335 A014336 A014337
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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