A087603 a(n) = (1/8)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*8^k.

1, 10, 155, 2100, 29525, 410750, 5731375, 79905000, 1114275625, 15537531250, 216660471875, 3021168937500, 42128015328125, 587444444843750, 8191485291484375, 114224297381250000, 1592774664844140625, 22210083004410156250, 309703436610529296875

Offset: 0

Author

Benoit Cloitre, Oct 25 2003

Keywords

• nonn
• easy

Comments

More generally a(n)=(1/x)*sum(k=0,n,binomial(n,k)*Fibonacci(k)*x^k) satisfies the recurrence formula a(n)=(x+2)*a(n-1)+(x^2-x-1)*a(n-2).

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..873
• Index entries for linear recurrences with constant coefficients, signature (10, 55).

Crossrefs

Cf. A014445, A057088, A015553.

Programs

Mathematica

LinearRecurrence[{10,55},{1,10},30] (* Harvey P. Dale, Nov 26 2014 *)

PARI

Vec(1/(1-10*x-55*x^2) + O(x^50)) \\ Colin Barker, Mar 30 2016

Formula

a(n) = 10*a(n-1)+55*a(n-2).

G.f.: -1/(-1+10*x+55*x^2). - R. J. Mathar, Dec 05 2007

a(n) = ((-(5-4*sqrt(5))^(1+n)+(5+4*sqrt(5))^(1+n)))/(8*sqrt(5)). - Colin Barker, Mar 30 2016