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A158766
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a(n) = 1444*n^2 + 38.
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2
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38, 1482, 5814, 13034, 23142, 36138, 52022, 70794, 92454, 117002, 144438, 174762, 207974, 244074, 283062, 324938, 369702, 417354, 467894, 521322, 577638, 636842, 698934, 763914, 831782, 902538, 976182, 1052714, 1132134, 1214442, 1299638, 1387722, 1478694, 1572554
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OFFSET
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0,1
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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 A158767(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*(1 + 36*x + 39*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(38))*Pi/sqrt(38) + 1)/76.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(38))*Pi/sqrt(38) + 1)/76. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {38, 1482, 5814}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
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PROG
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(Magma) I:=[38, 1482, 5814]; [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 21 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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