login
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
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)
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
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, May 29 2003
STATUS
approved