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 A082988 a(n) = Sum_{k=0..n} 4^k*F(k) where F(k) is the k-th Fibonacci number. 2
 0, 4, 20, 148, 916, 6036, 38804, 251796, 1628052, 10540948, 68212628, 441505684, 2857424788, 18493790100, 119693957012, 774676469652, 5013809190804, 32450060277652, 210021188163476, 1359285717096340, 8797481879000980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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) LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,12,-16). FORMULA 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 PROG (PARI) a(n)=if(n<0, 0, sum(k=0, n, fibonacci(k)*4^k)) CROSSREFS Cf. A014334, A082987, A119282. Sequence in context: A301270 A366183 A117887 * A001171 A247331 A167018 Adjacent sequences: A082985 A082986 A082987 * A082989 A082990 A082991 KEYWORD nonn,easy AUTHOR Benoit Cloitre, May 29 2003 STATUS approved

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Last modified June 15 16:36 EDT 2024. Contains 373410 sequences. (Running on oeis4.)