A146312 a(n) = -cos((2*n-1)*arcsin(sqrt(3)))^2 = -1 + cosh((2*n-1)*arcsinh(sqrt(2)))^2.

2, 242, 23762, 2328482, 228167522, 22358088722, 2190864527282, 214682365584962, 21036680962799042, 2061380051988721202, 201994208413931878802, 19793371044513335401442, 1939548368153892937462562, 190055946708036994535929682, 18623543229019471571583646322

Offset: 1

Author

Artur Jasinski, Oct 29 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

Crossrefs

Cf. A054320, A146311, A146313.

Programs

Mathematica

Table[Round[ -N[Cos[(2 n - 1) ArcSin[Sqrt[3]]], 300]^2], {n, 1, 50}]
LinearRecurrence[{99, -99, 1}, {2, 242, 23762}, 50] (* G. C. Greubel, Jul 03 2017 *)

PARI

Vec(-2*x*(x^2+22*x+1) / ((x-1)*(x^2-98*x+1)) + O(x^100)) \\ Colin Barker, Oct 26 2014

Formula

General formula: cosh((2*n-1)*arcsinh(sqrt(2)))^2 + cos((2*n-1)*arcsin(sqrt(3)))^2 = 1.

a(n) = A146313(n) - 1.

From Colin Barker, Oct 26 2014: (Start)

a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3).

G.f.: -2*x*(x^2+22*x+1) / ((x-1)*(x^2-98*x+1)). (End)

a(n) = 2*A054320(n-1)^2. - Jon E. Schoenfield, Jun 08 2018

Extensions

More terms from Colin Barker, Oct 26 2014