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A158764
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a(n) = 38*(38*n^2-1).
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2
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1406, 5738, 12958, 23066, 36062, 51946, 70718, 92378, 116926, 144362, 174686, 207898, 243998, 282986, 324862, 369626, 417278, 467818, 521246, 577562, 636766, 698858, 763838, 831706, 902462, 976106, 1052638, 1132058, 1214366, 1299562, 1387646, 1478618, 1572478
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OFFSET
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1,1
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COMMENTS
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The identity (76*n^2-1)^2 - (1444*n^2-38) * (2*n)^2 = 1 can be written as A158765(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.: 38*x*(-37-40*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(38))*Pi/sqrt(37))/76.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(37))*Pi/sqrt(38) - 1)/76. (End)
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MATHEMATICA
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Table[38 (38 n^2 - 1), {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {1406, 5738, 12958}, 40] (* Harvey P. Dale, Jan 09 2012 *)
CoefficientList[Series[38 (- 37 - 40 x + x^2) / (x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 11 2013 *)
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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 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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