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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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

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

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

MATHEMATICA

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

CROSSREFS

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

Cf. A084326.

Sequence in context: A272363 A283488 A006646 * A180038 A052896 A215128

Adjacent sequences: A087632 A087633 A087634 * A087636 A087637 A087638

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Oct 23 2003

STATUS

approved

URL: https://oeis.org/A087635

⇱ A087635 - OEIS