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A158547
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a(n) = 24*n^2 + 1.
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2
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1, 25, 97, 217, 385, 601, 865, 1177, 1537, 1945, 2401, 2905, 3457, 4057, 4705, 5401, 6145, 6937, 7777, 8665, 9601, 10585, 11617, 12697, 13825, 15001, 16225, 17497, 18817, 20185, 21601, 23065, 24577, 26137, 27745, 29401, 31105, 32857, 34657
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OFFSET
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0,2
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COMMENTS
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The identity (24*n^2 + 1)^2 - (144*n^2 + 12) * (2*n)^2 = 1 can be written as a(n)^2 - A158546(n) * A005843(n)^2 = 1.
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LINKS
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FORMULA
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G.f.: (1 + 22*x + 25*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = 1/2 + coth(Pi/(2*sqrt(6))*Pi/(4*sqrt(6)).
Sum_{n>=0} (-1)^n/a(n) = 1/2 + cosech(Pi/(2*sqrt(6))*Pi/(4*sqrt(6)). (End)
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MATHEMATICA
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PROG
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(Magma) I:=[1, 25, 97]; [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 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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STATUS
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approved
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