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a(n+1) = 4*a(n)^3 - 3*a(n), with a(0) = 2.
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%I #43 Feb 25 2018 15:53:35

%S 2,26,70226,1385331749802026,

%T 10634604778476758291777057017318241822792488226

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

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

%C Term a(5) has 139 decimal digits and a(6) has 417 decimal digits. - _Andrew Howroyd_, Feb 25 2018

%H Andrew Howroyd, <a href="/A094680/b094680.txt">Table of n, a(n) for n = 0..6</a>

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

%F a(n) = ChebyshevT(3^n, 2). - _Vladeta Jovovic_, Jun 11 2004

%F From _A.H.M. Smeets_, Oct 02 2017: (Start)

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

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

%t NestList[4 #^3 - 3 # &, 2, 5] (* _Michael De Vlieger_, Oct 02 2017 *)

%o (PARI) a(n) = if (n==0, 2, 4*a(n-1)^3 - 3*a(n-1)); \\ _Michel Marcus_, Oct 03 2017

%o (PARI) a(n) = polchebyshev(3^n, 1, 2); \\ _Michel Marcus_, Oct 03 2017

%Y Cf. A001075, A002812.

%K nonn,easy

%O 0,1

%A _Jose Eduardo Blazek_, Jun 07 2004

%E More terms from _Vladeta Jovovic_, Jun 11 2004

%E Offset corrected by _Michel Marcus_, Oct 03 2017