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A084328 a(0)=0, a(1)=1; a(n) = 13*a(n-1) - 11*a(n-2). 0
0, 1, 13, 158, 1911, 23105, 279344, 3377317, 40832337, 493669894, 5968552915, 72160819061, 872436565728, 10547906344793, 127525980259301, 1541810773578190, 18640754273664159, 225369887048273977 (list; graph; refs; listen; history; text; internal format)
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.

a(n) = -(1/25)*(13/2 - (5/2)*sqrt(5))^n*sqrt(5) + (1/25)*sqrt(5)*(13/2 + (5/2)*sqrt(5))^n, with n >= 0. - Paolo P. Lava, Jun 19 2008

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 xrange(0, 18)] # Zerinvary Lajos, Apr 29 2009

CROSSREFS

Cf. A030191.

Sequence in context: A016125 A175519 A015470 * A000830 A205170 A205163

Adjacent sequences:  A084325 A084326 A084327 * A084329 A084330 A084331

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Jun 21 2003

STATUS

approved

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Last modified November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)