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A158633
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a(n) = 529*n^2 - 23.
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2
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506, 2093, 4738, 8441, 13202, 19021, 25898, 33833, 42826, 52877, 63986, 76153, 89378, 103661, 119002, 135401, 152858, 171373, 190946, 211577, 233266, 256013, 279818, 304681, 330602, 357581, 385618, 414713, 444866, 476077, 508346, 541673, 576058, 611501, 648002
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OFFSET
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1,1
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COMMENTS
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The identity (46*n^2-1)^2-(529*n^2-23)*(2*n)^2 = 1 can be written as A158634(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.: 23*x*(-22-25*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(23))*Pi/sqrt(23))/46.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(23))*Pi/sqrt(23) - 1)/46. (End)
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MAPLE
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MATHEMATICA
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a[n_] := 529*n^2 - 23; Array[a, 50] (* Amiram Eldar, Mar 16 2023 *)
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PROG
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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 rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
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STATUS
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approved
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