A087635 a(n) = S(n,3) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).

0, 2, 12, 64, 336, 1760, 9216, 48256, 252672, 1323008, 6927360, 36272128, 189923328, 994451456, 5207015424, 27264286720, 142757658624, 747488804864, 3913902194688, 20493457948672, 107305138913280, 561857001684992

Offset: 0

Author

Benoit Cloitre, Oct 23 2003

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-4).

Crossrefs

Cf. A000045, A001906 (S(n, 1)), A030191 (S(n, 2)).

Cf. A084326.

Programs

Mathematica

LinearRecurrence[{6,-4}, {0, 2}, 22] (* Amiram Eldar, Apr 29 2025 *)

Formula

a(n) = 6*a(n-1)-4*a(n-2) = 2*A084326(n).

a(n) = Sum_{0<=j<=i<=n} C(i,j)*C(n,i)*Fibonacci(i+j). - Benoit Cloitre, May 21 2005

a(n) = 2^n*Fibonacci(2*n). - Benoit Cloitre, Sep 13 2005

a(n) = Sum_{k=0..n} C(n,k)*Fibonacci(k)*Lucas(n-k). - Ross La Haye, Aug 14 2006

G.f.: 2*x/(1-6*x+4*x^2). - Colin Barker, Jun 19 2012