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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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2
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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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COMMENTS
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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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LINKS
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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, Dec 05 2007
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PROG
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(PARI) a(n)=if(n<0, 0, sum(k=0, n, fibonacci(k)*4^k))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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