The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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)
LINKS
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
Sequence in context: A301270 A366183 A117887 * A001171 A247331 A167018
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, May 29 2003
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 16:36 EDT 2024. Contains 373410 sequences. (Running on oeis4.)