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A158558
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a(n) = 30*n^2 + 1.
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5
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1, 31, 121, 271, 481, 751, 1081, 1471, 1921, 2431, 3001, 3631, 4321, 5071, 5881, 6751, 7681, 8671, 9721, 10831, 12001, 13231, 14521, 15871, 17281, 18751, 20281, 21871, 23521, 25231, 27001, 28831, 30721, 32671, 34681, 36751, 38881, 41071, 43321, 45631, 48001, 50431
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OFFSET
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0,2
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COMMENTS
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The identity (30*n^2+1)^2 - (225*n^2+15)*(2*n)^2 = 1 can be written as a(n)^2 - A158557(n)*A005843(n)^2 = 1.
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LINKS
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FORMULA
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G.f.: (1 + 28*x + 31*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(30))*Pi/sqrt(30) + 1)/2.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(30))*Pi/sqrt(30) + 1)/2. (End)
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MATHEMATICA
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PROG
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(Magma) I:=[1, 31, 121]; [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 14 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, and a(0) added by R. J. Mathar, Oct 16 2009
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STATUS
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approved
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