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A146313
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a(n) = cosh( (2n - 1)*arcsinh(sqrt(2)) )^2 = 1 - cos( (2n - 1)*arcsin(sqrt(3)) )^2.
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25
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3, 243, 23763, 2328483, 228167523, 22358088723, 2190864527283, 214682365584963, 21036680962799043, 2061380051988721203, 201994208413931878803, 19793371044513335401443, 1939548368153892937462563, 190055946708036994535929683, 18623543229019471571583646323
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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MAPLE
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A146313 := proc(n) cosh( (2*n - 1)*arcsinh(sqrt(2)) )^2; expand(%) ; simplify(%) ; end proc: # R. J. Mathar, Feb 26 2011
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MATHEMATICA
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Table[Round[N[Cosh[(2 n - 1) ArcSinh[Sqrt[2]]], 300]^2], {n, 1, 50}] (* Artur Jasinski, Oct 30 2008 *)
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PROG
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(PARI) Vec(-3*x*(x^2-18*x+1) / ((x-1)*(x^2-98*x+1)) + O(x^100)) \\ Colin Barker, Oct 26 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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