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