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

1, 13, 7778742049, 215414832505658809004682396169711233230800418578767753330908886771798637

Offset

0,2

Links

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

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}]

Prog

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

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).

Sequence in context: A174309 A081509 A177224 * A334634 A048847 A093671

Adjacent sequences: A145231 A145232 A145233 * A145235 A145236 A145237

Keyword

nonn,easy

Author

Artur Jasinski, Oct 05 2008

Status

approved