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A146312
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a(n) = -cos((2 n - 1) arcsin(sqrt(3)))^2 = -1 + cosh((2 n - 1) arcsinh(sqrt(2)))^2.
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21
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2, 242, 23762, 2328482, 228167522, 22358088722, 2190864527282, 214682365584962, 21036680962799042, 2061380051988721202, 201994208413931878802, 19793371044513335401442, 1939548368153892937462562, 190055946708036994535929682, 18623543229019471571583646322
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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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General formula: cosh((2*n-1)*arcsinh(sqrt(2)))^2 + cos((2*n-1)*arcsin(sqrt(3))^2 = 1.
a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3). - Colin Barker, Oct 26 2014
G.f.: -2*x*(x^2+22*x+1) / ((x-1)*(x^2-98*x+1)). - Colin Barker, Oct 26 2014
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MATHEMATICA
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Table[Round[ -N[Cos[(2 n - 1) ArcSin[Sqrt[3]]], 300]^2], {n, 1, 50}]
LinearRecurrence[{99, -99, 1}, {2, 242, 23762}, 50] (* G. C. Greubel, Jul 03 2017 *)
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PROG
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(PARI) Vec(-2*x*(x^2+22*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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