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A158729
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a(n) = 1156*n^2 - 34.
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2
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1122, 4590, 10370, 18462, 28866, 41582, 56610, 73950, 93602, 115566, 139842, 166430, 195330, 226542, 260066, 295902, 334050, 374510, 417282, 462366, 509762, 559470, 611490, 665822, 722466, 781422, 842690, 906270, 972162, 1040366, 1110882, 1183710, 1258850, 1336302
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OFFSET
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1,1
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COMMENTS
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The identity (68*n^2 - 1)^2 - (1156*n^2 - 34)*(2*n)^2 = 1 can be written as A158730(n)^2 - a(n)*A005843(n)^2 = 1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
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FORMULA
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G.f.: 34*x*(-33 - 36*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(34))*Pi/sqrt(34))/68.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(34))*Pi/sqrt(34) - 1)/68. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1122, 4590, 10370}, 50] (* Vincenzo Librandi, Feb 20 2012 *)
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PROG
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(Magma) I:=[1122, 4590, 10370]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 20 2012
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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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Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009
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STATUS
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approved
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