A146313 a(n) = cosh( (2n - 1)*arcsinh(sqrt(2)) )^2 = 1 - cos( (2n - 1)*arcsin(sqrt(3)) )^2.

3, 243, 23763, 2328483, 228167523, 22358088723, 2190864527283, 214682365584963, 21036680962799043, 2061380051988721203, 201994208413931878803, 19793371044513335401443, 1939548368153892937462563, 190055946708036994535929683, 18623543229019471571583646323

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. A146311, A146312.

Programs

Maple

A146313 := proc(n) cosh( (2*n - 1)*arcsinh(sqrt(2)) )^2; expand(%) ; simplify(%) ; end proc: # R. J. Mathar, Feb 26 2011

Mathematica

Table[Round[N[Cosh[(2 n - 1) ArcSinh[Sqrt[2]]], 300]^2], {n, 1, 50}] (* Artur Jasinski, Oct 30 2008 *)

PARI

Vec(-3*x*(x^2-18*x+1) / ((x-1)*(x^2-98*x+1)) + O(x^100)) \\ Colin Barker, Oct 26 2014

Formula

a(n) = A146312(n) + 1.

a(n) = sin((2n-1)*arcsin(sqrt(3)))^2 = 1+sinh((2n-1)*arcsinh(sqrt(2)))^2. - Artur Jasinski, Oct 30 2008

a(n) = 99*a(n-1)-99*a(n-2)+a(n-3). - Colin Barker, Oct 26 2014

G.f.: -3*x*(x^2-18*x+1) / ((x-1)*(x^2-98*x+1)). - Colin Barker, Oct 26 2014

Extensions

More terms from Colin Barker, Oct 26 2014