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A158586
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a(n) = 34*n^2 + 1.
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2
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1, 35, 137, 307, 545, 851, 1225, 1667, 2177, 2755, 3401, 4115, 4897, 5747, 6665, 7651, 8705, 9827, 11017, 12275, 13601, 14995, 16457, 17987, 19585, 21251, 22985, 24787, 26657, 28595, 30601, 32675, 34817, 37027, 39305, 41651, 44065, 46547, 49097, 51715, 54401, 57155
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OFFSET
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0,2
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COMMENTS
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The identity (34*n^2 + 1)^2 - (289*n^2 + 17)*(2*n)^2 = 1 can be written as a(n)^2 - A158585(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.: (1 + 32*x + 35*x^2)/(1-x)^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)/2.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(34))*Pi/sqrt(34) + 1)/2. (End)
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MATHEMATICA
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PROG
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(Magma) I:=[1, 35, 137]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 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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STATUS
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approved
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