A146311 a(n) = cos(2*n*arcsin(sqrt(3))) = (-1)^n*cosh(2*n*arcsinh(sqrt(2))).

1, -5, 49, -485, 4801, -47525, 470449, -4656965, 46099201, -456335045, 4517251249, -44716177445, 442644523201, -4381729054565, 43374646022449, -429364731169925, 4250272665676801, -42073361925598085, 416483346590304049

Offset: 0

Author

Artur Jasinski, Oct 29 2008

Keywords

• sign
• easy

Comments

Apart from sign, same as A001079 (see first formula).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-10,-1).

Crossrefs

Cf. A001079.

Programs

Mathematica

Table[Round[N[Cos[2 n ArcSin[Sqrt[3]]], 50]], {n, 0, 100}]
CoefficientList[Series[(5*x + 1)/(x^2 + 10*x + 1), {x,0,50}], x] (* G. C. Greubel, Jul 02 2017 *)

PARI

Vec((5*x+1)/(x^2+10*x+1) + O(x^100)) \\ Colin Barker, Oct 26 2014

Formula

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)

E.g.f.: exp(-5*x)*cosh(2*sqrt(6)*x). - Stefano Spezia, Feb 14 2025

Extensions

a(18) from Colin Barker, Oct 26 2014