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%I #19 Dec 28 2023 19:34:15
%S 1,-5,49,-485,4801,-47525,470449,-4656965,46099201,-456335045,
%T 4517251249,-44716177445,442644523201,-4381729054565,43374646022449,
%U -429364731169925,4250272665676801,-42073361925598085,416483346590304049
%N a(n) = cos(2*n*arcsin(sqrt(3))) = (-1)^n*cosh(2*n*arcsinh(sqrt(2))).
%C Apart from sign, same as A001079 (see first formula).
%H G. C. Greubel, <a href="/A146311/b146311.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-10,-1).
%F a(n) = (-1)^n * A001079(n).
%F From _Colin Barker_, Oct 26 2014: (Start)
%F a(n) = ((-5-2*sqrt(6))^n + (-5+2*sqrt(6))^n)/2.
%F a(n) = -10*a(n-1)-a(n-2).
%F G.f.: (5*x+1) / (x^2+10*x+1).
%F (End)
%t Table[Round[N[Cos[2 n ArcSin[Sqrt[3]]], 50]], {n, 0, 100}]
%t CoefficientList[Series[(5*x + 1)/(x^2 + 10*x + 1), {x,0,50}], x] (* _G. C. Greubel_, Jul 02 2017 *)
%o (PARI) Vec((5*x+1)/(x^2+10*x+1) + O(x^100)) \\ _Colin Barker_, Oct 26 2014
%Y Cf. A001079.
%K sign,easy
%O 0,2
%A _Artur Jasinski_, Oct 29 2008
%E a(18) from _Colin Barker_, Oct 26 2014