A082988 a(n) = Sum_{k=0..n} 4^k*F(k) where F(k) is the k-th Fibonacci number.
0, 4, 20, 148, 916, 6036, 38804, 251796, 1628052, 10540948, 68212628, 441505684, 2857424788, 18493790100, 119693957012, 774676469652, 5013809190804, 32450060277652, 210021188163476, 1359285717096340, 8797481879000980
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,12,-16).
Programs
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Mathematica
LinearRecurrence[{5, 12, -16}, {0, 4, 20}, 21] (* Amiram Eldar, Apr 29 2025 *) -
PARI
a(n)=if(n<0,0,sum(k=0,n,fibonacci(k)*4^k));
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
Comments