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

2, 26, 70226, 1385331749802026, 10634604778476758291777057017318241822792488226

Offset

0,1

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

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A001075, A002812.

Sequence in context: A268667 A330032 A273381 * A259326 A061192 A356136

Adjacent sequences: A094677 A094678 A094679 * A094681 A094682 A094683

Keyword

nonn,easy

Author

Jose Eduardo Blazek, Jun 07 2004

Extensions

More terms from Vladeta Jovovic, Jun 11 2004

Offset corrected by Michel Marcus, Oct 03 2017

Status

approved