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Search: id:A082988
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| A082988 |
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a(n)=sum(k=0,n,4^k*F(k)) where F(k) is the k-th Fibonacci number. |
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+0
1
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| 0, 4, 20, 148, 916, 6036, 38804, 251796, 1628052, 10540948, 68212628, 441505684, 2857424788, 18493790100, 119693957012, 774676469652, 5013809190804, 32450060277652, 210021188163476, 1359285717096340, 8797481879000980
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OFFSET
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0,2
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COMMENT
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More generally for any complex number z, sequence a(n)=sum(k=0,n,z^k*F(k)) satisfies the recurrence : a(0)=0, a(1)=z, a(2)=z(z+1), for n>2 a(n)=(z+1)*a(n-1)+z*(z-1)*a(n-2)-z^2*a(n-3)
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FORMULA
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a(0)=0, a(1)=4, a(2)=20, a(n)=5a(n-1)+12a(n-2)-16a(n-3)
O.g.f.: 4*x/((x-1)*(16*x^2+4*x-1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
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PROGRAM
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(PARI) a(n)=if(n<0, 0, sum(k=0, n-1, fibonacci(k)*4^k))
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CROSSREFS
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Cf. A014334.
Sequence in context: A034216 A144009 A117887 this_sequence A001171 A167018 A094070
Adjacent sequences: A082985 A082986 A082987 this_sequence A082989 A082990 A082991
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 29 2003
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