OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..950
Michael D.Hirschhorn, A Naive Proof that F5n = 0 (mod 5), Fib. Q. 51(3), 2013, 256-258.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (11,1).
FORMULA
G.f.: 5*x/(1-11*x-x^2).
a(n) = Fibonacci(2*n)*Lucas(3*n)+Fibonacci(n). Lucas =A000032(n), Fibonacci=A000045(n). - Gary Detlefs, Dec 22 2012
a(n) = (-((11 - 5*sqrt(5))/2)^n + ((11+5*sqrt(5))/2)^n)/sqrt(5). - Colin Barker, Nov 10 2016
a(n) = 11*a(n-1)+a(n-2). - Mike Speciner, Aug 20 2024
MAPLE
seq(combinat:-fibonacci(5*n), n=0..100); # Robert Israel, Dec 12 2014
MATHEMATICA
Table[ Fibonacci[5n], {n, 0, 17}] (* Robert G. Wilson v, Jan 09 2005 *)
PROG
(Sage) [fibonacci(5*n) for n in range(0, 18)] # Zerinvary Lajos, May 15 2009
(Magma) [Fibonacci(5*n): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011
(PARI) vector(18, n, fibonacci(5*n)) \\ Edward Jiang, Dec 11 2014
(PARI) concat(0, Vec(5*x/(1-11*x-x^2) + O(x^30))) \\ Colin Barker, Nov 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Jan 06 2005
STATUS
approved