OFFSET
1,2
COMMENTS
The ratio of two consecutive terms of this sequence, as n goes to infinity, is phi^6 = 8*phi+5 = 9+4*sqrt(5) where phi is the golden ratio=1.618...
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (20,-35,-35,20,-1).
FORMULA
a(n) = 20*a(n-1) - 35*a(n-2) - 35*a(n-3) + 20*a(n-4) - a(n-5). - R. J. Mathar, Nov 23 2010
G.f.: x*(1-14*x-31*x^2+22*x^3-2*x^4) / ((1+x)*(x^2-3*x+1)*(x^2-18*x+1)).
EXAMPLE
d(3) = 54 since F(7)^3 = F(9)^2 + F(16) + 54.
MATHEMATICA
Table[(1/5)*(3*Fibonacci[2*n + 1] + Fibonacci[6*n - 5] + 2*(-1)^n), {n, 1, 10}] (* G. C. Greubel, Apr 18 2016 *)
LinearRecurrence[{20, -35, -35, 20, -1}, {1, 6, 54, 857, 15058}, 20] (* Harvey P. Dale, Dec 15 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Carmine Suriano, Dec 15 2009
EXTENSIONS
Simplified the definition. - N. J. A. Sloane, Nov 24 2010
STATUS
approved