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A158773
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a(n) = 1600*n^2 - 40.
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2
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1560, 6360, 14360, 25560, 39960, 57560, 78360, 102360, 129560, 159960, 193560, 230360, 270360, 313560, 359960, 409560, 462360, 518360, 577560, 639960, 705560, 774360, 846360, 921560, 999960, 1081560, 1166360, 1254360, 1345560, 1439960, 1537560, 1638360, 1742360
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OFFSET
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1,1
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COMMENTS
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The identity (80*n^2 - 1)^2 - (1600*n^2 - 40)*(2*n)^2 = 1 can be written as A158774(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.: 40*x*(-39 - 42*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/(2*sqrt(10)))*Pi/(2*sqrt(10)))/80.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(2*sqrt(10)))*Pi/(2*sqrt(10)) - 1)/80. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1560, 6360, 14360}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
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PROG
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(Magma) I:=[1560, 6360, 14360]; [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 21 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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