OFFSET
1,1
COMMENTS
a(n+1)/a(n) -> (phi)^3 = ((1 + sqrt(5))/2)^3 = 4.236067...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..160
C. Pita, On s-Fibonomials, J. Int. Seq. 14 (2011) # 11.3.7
Index entries for linear recurrences with constant coefficients, signature (3, 6, -3, -1).
FORMULA
From Benoit Cloitre, Aug 30 2003: (Start)
a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4);
a(n) = Lucas(3*n) + (-1)^n*Lucas(n).
From R. J. Mathar, Oct 27 2008: (Start)
G.f.: x*(3+12*x-9*x^2-4*x^3)/((1+x-x^2)*(1-4*x-x^2)).
a(n) = (1+phi)^n + (-phi)^n + (2*phi+1)^n + (3-2*phi)^n, phi = (1+sqrt(5))/2. - Gary Detlefs, Dec 09 2012
EXAMPLE
a(4) = Lucas(4)*Lucas(8) = 7*47 = 329.
MATHEMATICA
Table[Fibonacci[n*4]/Fibonacci[n], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)
PROG
(Magma) [Lucas(n)*Lucas(2*n): n in [1..25]]; // Vincenzo Librandi, May 03 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 12 2003
STATUS
approved