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A145678
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a(n) = 441*n^2 - 21.
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2
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420, 1743, 3948, 7035, 11004, 15855, 21588, 28203, 35700, 44079, 53340, 63483, 74508, 86415, 99204, 112875, 127428, 142863, 159180, 176379, 194460, 213423, 233268, 253995, 275604, 298095, 321468, 345723, 370860, 396879, 423780, 451563
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OFFSET
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1,1
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COMMENTS
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The identity (42*n^2 - 1)^2 - (441*n^2 - 21)*(2*n)^2 = 1 can be written as A158626(n)^2 - a(n)*A005843(n)^2 = 1.
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LINKS
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FORMULA
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G.f.: -21*x*(20 + 23*x - x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(21))*Pi/sqrt(21))/42.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(21))*Pi/sqrt(21) - 1)/42. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {420, 1743, 3948}, 50] (* Vincenzo Librandi, Feb 12 2012 *)
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PROG
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(Magma) I:=[420, 1743, 3948]; [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 12 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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STATUS
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approved
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