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A014334
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Exponential convolution of Fibonacci numbers with themselves.
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5
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,2,-4).
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FORMULA
| 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
a(n) = 2*A014335(n). G.f.: 2*x^2/((x-1)*(4*x^2+2*x-1)). a(n)= sum_{k=1..n-1} A103435(k). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2010]
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MATHEMATICA
| Join[{a=0, b=0}, Table[c=2*b+4*a+2; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
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PROG
| (PARI) a(n)=if(n<1, 0, sum(k=0, n-1, fibonacci(k)*2^k))
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CROSSREFS
| Cf. A000045, A103435.
Sequence in context: A126171 A002839 A109194 * A107239 A148496 A181367
Adjacent sequences: A014331 A014332 A014333 * A014335 A014336 A014337
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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