A145234 a(n) = Fibonacci(7^n).

1, 13, 7778742049, 215414832505658809004682396169711233230800418578767753330908886771798637

Offset: 0

Author

Artur Jasinski, Oct 05 2008

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..4

Crossrefs

Cf. A000045.

Cf. (k^n)-th Fibonacci number: A058635 (k=2), A045529 (k=3), A145231 (k=4), A145232 (k=5), A145233 (k=6), this sequence (k=7), A250487 (k=8), A250488 (k=9), A250489 (k=10).

Programs

Magma

[Fibonacci(7^n): n in [0..5]]; // Vincenzo Librandi, Apr 02 2011

Maple

A145234 := proc(n) combinat[fibonacci](7^n) ; end proc:
seq(A145234(n),n=1..3) ; # R. J. Mathar, Apr 01 2011

Mathematica

G = (1 + Sqrt[5])/2; Table[Expand[(G^(7^n) - (1 - G)^(7^n))/Sqrt[5]], {n, 1, 6}]
(* Second program: *)
Table[Round[N[(2/Sqrt[5])*Cosh[7^n*ArcCosh[Sqrt[5]/2]], 1000]], {n, 1, 4}]

Formula

a(n) = (G^(7^n) - (1 - G)^(7^n))/sqrt(5) where G = (1 + sqrt(5))/2.

a(n) = (2/sqrt(5))*cosh(7^n*arccosh(sqrt(5)/2)).

a(n+1) = 125*a(n)^7 - 175*a(n)^5 + 70*a(n)^3 - 7*a(n) with a(0) = 1. - Peter Bala, Nov 25 2022