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Table[Round[N[Cos[2 n ArcSin[Sqrt[3]]], 50]], {n, 0, 100}] (* _Artur Jasinski_*)
editing
proposed
proposed
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proposed
a(n) = Cos[2n ArcSin[Sqrt[3]] = (-1)^n Cosh[2n ArcSinh[Sqrt[2]].
1, -5, 49, -485, 4801, -47525, 470449, -4656965, 46099201, -456335045, 4517251249, -44716177445, 442644523201, -4381729054565, 43374646022449, -429364731169925, 4250272665676801, -42073361925598085, 416483346590304049
<a href="/index/Rec#order_02">Index to sequences with linear recurrences with constant coefficients</a>, signature (-10,-1).
a(n) = (-1)^n A001079(n).
From Colin Barker, Oct 26 2014: (Start)
a(n) = ((-5-2*sqrt(6))^n+(-5+2*sqrt(6))^n)/2.
a(n) = -10*a(n-1)-a(n-2).
G.f.: (5*x+1) / (x^2+10*x+1).
(End)
(PARI) Vec((5*x+1)/(x^2+10*x+1) + O(x^100)) \\ Colin Barker, Oct 26 2014
Cf. A001079.
sign,easy
a(18) from Colin Barker, Oct 26 2014
approved
editing
_Artur Jasinski (grafix(AT)csl.pl), _, Oct 29 2008
a(n) = Cos[2n ArcSin[Sqrt[3]] = (-1)^n Cosh[2n ArcSinh[Sqrt[2]]
1, -5, 49, -485, 4801, -47525, 470449, -4656965, 46099201, -456335045, 4517251249, -44716177445, 442644523201, -4381729054565, 43374646022449, -429364731169925, 4250272665676801, -42073361925598085
0,2
a(n)=(-1)^n A001079(n).
Table[Round[N[Cos[2 n ArcSin[Sqrt[3]]], 50]], {n, 0, 100}] (*Artur Jasinski*)
sign
Artur Jasinski (grafix(AT)csl.pl), Oct 29 2008
approved