A094680 a(n+1) = 4*a(n)^3 - 3*a(n), with a(0) = 2.

2, 26, 70226, 1385331749802026, 10634604778476758291777057017318241822792488226

Offset: 0

Author

Jose Eduardo Blazek, Jun 07 2004

Keywords

• nonn
• easy

Comments

Smallest positive integer x satisfying the Pell equation x^2 - 3^(2*n-3) * y^2 = 1. - A.H.M. Smeets, Sep 29 2017

Term a(5) has 139 decimal digits and a(6) has 417 decimal digits. - Andrew Howroyd, Feb 25 2018

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..6

Crossrefs

Cf. A001075, A002812.

Programs

Mathematica

NestList[4 #^3 - 3 # &, 2, 5] (* Michael De Vlieger, Oct 02 2017 *)

PARI

a(n) = if (n==0, 2, 4*a(n-1)^3 - 3*a(n-1)); \\ Michel Marcus, Oct 03 2017

PARI

a(n) = polchebyshev(3^n, 1, 2); \\ Michel Marcus, Oct 03 2017

Formula

a(n) = cosh(3^n*arccosh(2)).

a(n) = ChebyshevT(3^n, 2). - Vladeta Jovovic, Jun 11 2004

From A.H.M. Smeets, Oct 02 2017: (Start)

a(n) = A001075(3^(n-2))

a(n) = A002350(3^(2n-3)). (End)

Extensions

More terms from Vladeta Jovovic, Jun 11 2004

Offset corrected by Michel Marcus, Oct 03 2017