OFFSET
0,2
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).
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
MATHEMATICA
LinearRecurrence[{10, 55}, {1, 10}, 30] (* Harvey P. Dale, Nov 26 2014 *)
PROG
(PARI) Vec(1/(1-10*x-55*x^2) + O(x^50)) \\ Colin Barker, Mar 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Oct 25 2003
STATUS
approved