A082987 a(n) = Sum_{k=0..n} 3^k*F(k) where F(k) is the k-th Fibonacci number.

0, 3, 12, 66, 309, 1524, 7356, 35787, 173568, 842790, 4090485, 19856568, 96384072, 467861331, 2271040644, 11023873914, 53510987541, 259747827852, 1260842371428, 6120257564955, 29708354037720, 144207380197758

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,6,-9).

Formula

a(0)=0, a(1)=3, a(2)=12, a(n)=4a(n-1)+6a(n-2)-9a(n-3).

G.f.: 3*x / ((x-1)*(9*x^2+3*x-1)). - Colin Barker, Jun 26 2013

Mathematica

LinearRecurrence[{4, 6, -9}, {0, 3, 12}, 30] (* Harvey P. Dale, Feb 03 2019 *)

Prog

(PARI) a(n)=if(n<0, 0, sum(k=0, n, fibonacci(k)*3^k))

Crossrefs

Cf. A014334, A082988, A119282.

Sequence in context: A144297 A007017 A183273 * A086836 A074513 A290147

Adjacent sequences: A082984 A082985 A082986 * A082988 A082989 A082990

Keyword

nonn,easy

Author

Benoit Cloitre, May 29 2003

Extensions

Offset changed to 0 by Seiichi Manyama, Oct 03 2023

Status

approved