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

Author

Benoit Cloitre, May 29 2003

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,6,-9).

Crossrefs

Cf. A014334, A082988, A119282.

Programs

Mathematica

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

PARI

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

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

Extensions

Offset changed to 0 by Seiichi Manyama, Oct 03 2023