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%I #22 Jul 01 2017 02:16:38
%S 3,243,23763,2328483,228167523,22358088723,2190864527283,
%T 214682365584963,21036680962799043,2061380051988721203,
%U 201994208413931878803,19793371044513335401443,1939548368153892937462563,190055946708036994535929683,18623543229019471571583646323
%N a(n) = cosh( (2n - 1)*arcsinh(sqrt(2)) )^2 = 1 - cos( (2n - 1)*arcsin(sqrt(3)) )^2.
%H G. C. Greubel, <a href="/A146313/b146313.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F a(n) = A146312(n) + 1.
%F a(n) = sin((2n-1)*arcsin(sqrt(3)))^2 = 1+sinh((2n-1)*arcsinh(sqrt(2)))^2. - _Artur Jasinski_, Oct 30 2008
%F a(n) = 99*a(n-1)-99*a(n-2)+a(n-3). - _Colin Barker_, Oct 26 2014
%F G.f.: -3*x*(x^2-18*x+1) / ((x-1)*(x^2-98*x+1)). - _Colin Barker_, Oct 26 2014
%p A146313 := proc(n) cosh( (2*n - 1)*arcsinh(sqrt(2)) )^2; expand(%) ; simplify(%) ; end proc: # _R. J. Mathar_, Feb 26 2011
%t Table[Round[N[Cosh[(2 n - 1) ArcSinh[Sqrt[2]]], 300]^2], {n, 1, 50}] (* _Artur Jasinski_, Oct 30 2008 *)
%o (PARI) Vec(-3*x*(x^2-18*x+1) / ((x-1)*(x^2-98*x+1)) + O(x^100)) \\ _Colin Barker_, Oct 26 2014
%Y Cf. A146311, A146312.
%K nonn,easy
%O 1,1
%A _Artur Jasinski_, Oct 29 2008
%E More terms from _Colin Barker_, Oct 26 2014