OFFSET
0,3
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).
FORMULA
a(n) = F(n-1)*(2*F(n+1)^2+(-1)^(n+1)), n>0.
a(n) = F(n-1)*A061646(n+1).
G.f.: (x-1)*(x^2+2*x-1)/((x^2+4*x-1)*(x^2-x-1)). - Alois P. Heinz, Jul 21 2021
For n >= 2, a(n) is the numerator of the continued fraction [1,...,1, 3 ,1,...,1, 2 ,1,...,1] with three runs of 1's each of length n-2. For example, a(5)=387 which is the numerator of the continued fraction [1,1,1, 3 ,1,1,1, 2 ,1,1,1]. - Greg Dresden, Jan 01 2022
MATHEMATICA
Differences[Fibonacci[Range[0, 26]]^3] (* Amiram Eldar, Jul 22 2021 *)
PROG
(PARI) a(n) = fibonacci(n+1)^3 - fibonacci(n)^3; \\ Michel Marcus, Jul 22 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lamine Ngom, Jul 21 2021
STATUS
approved