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A158629
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a(n) = 484*n^2 + 22.
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2
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22, 506, 1958, 4378, 7766, 12122, 17446, 23738, 30998, 39226, 48422, 58586, 69718, 81818, 94886, 108922, 123926, 139898, 156838, 174746, 193622, 213466, 234278, 256058, 278806, 302522, 327206, 352858, 379478, 407066, 435622, 465146, 495638, 527098, 559526, 592922
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OFFSET
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0,1
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COMMENTS
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The identity (44*n^2 + 1)^2 - (484*n^2 + 22)*(2*n)^2 = 1 can be written as A158630(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.: -22*(1 + 20*x + 23*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(22))*Pi/sqrt(22) + 1)/44.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(22))*Pi/sqrt(22) + 1)/44. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {22, 506, 1958}, 50] (* Vincenzo Librandi, Feb 17 2012 *)
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PROG
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(Magma) I:=[22, 506, 1958]; [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 17 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, formula replaced by R. J. Mathar, Oct 28 2009
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STATUS
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approved
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