A084328 a(0)=0, a(1)=1; a(n) = 13*a(n-1) - 11*a(n-2).

0, 1, 13, 158, 1911, 23105, 279344, 3377317, 40832337, 493669894, 5968552915, 72160819061, 872436565728, 10547906344793, 127525980259301, 1541810773578190, 18640754273664159, 225369887048273977

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (13,-11).

Formula

a(n) = (1/5)*Sum_{k=0..n} binomial(n, k)*F(5*k) where F(k) denotes the k-th Fibonacci number.

G.f.: x / (11*x^2-13*x+1). - Colin Barker, Jun 26 2013

Mathematica

Join[{a=0, b=1}, Table[c=13*b-11*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 21 2011 *)

Prog

(PARI) a(n)=(1/5)*sum(k=0, n, binomial(n, k)*fibonacci(5*k));
(Sage) [lucas_number1(n, 13, 11) for n in range(0, 18)] # Zerinvary Lajos, Apr 29 2009

Crossrefs

Cf. A030191.

Sequence in context: A353147 A175519 A015470 * A000830 A205170 A205163

Adjacent sequences: A084325 A084326 A084327 * A084329 A084330 A084331

Keyword

nonn,easy

Author

Benoit Cloitre, Jun 21 2003

Status

approved