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A158731
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a(n) = 1156*n^2 + 34.
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2
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34, 1190, 4658, 10438, 18530, 28934, 41650, 56678, 74018, 93670, 115634, 139910, 166498, 195398, 226610, 260134, 295970, 334118, 374578, 417350, 462434, 509830, 559538, 611558, 665890, 722534, 781490, 842758, 906338, 972230, 1040434, 1110950, 1183778, 1258918
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OFFSET
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0,1
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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 A158732(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*(1 + 32*x + 35*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(34))*Pi/sqrt(34) + 1)/68.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(34))*Pi/sqrt(34) + 1)/68. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {34, 1190, 4658}, 50] (* Vincenzo Librandi, Feb 20 2012 *)
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PROG
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(Magma) I:=[34, 1190, 4658]; [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, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009
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STATUS
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approved
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