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A158683
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a(n) = 1024*n^2 - 32.
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2
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992, 4064, 9184, 16352, 25568, 36832, 50144, 65504, 82912, 102368, 123872, 147424, 173024, 200672, 230368, 262112, 295904, 331744, 369632, 409568, 451552, 495584, 541664, 589792, 639968, 692192, 746464, 802784, 861152, 921568, 984032, 1048544, 1115104, 1183712
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OFFSET
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1,1
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COMMENTS
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The identity (64*n^2-1)^2-(1024*n^2-32)*(2*n)^2 = 1 can be written as A158684(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.: 32*x*(-31-34*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/(4*sqrt(2)))*Pi/(4*sqrt(2)))/64.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(4*sqrt(2)))*Pi/(4*sqrt(2)) - 1)/64. (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {992, 4064, 9184}, 50] (* Vincenzo Librandi, Feb 19 2012 *)
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PROG
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(Magma) I:=[992, 4064, 9184]; [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 19 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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