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A157909
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a(n) = 81*n^2 - 9.
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3
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72, 315, 720, 1287, 2016, 2907, 3960, 5175, 6552, 8091, 9792, 11655, 13680, 15867, 18216, 20727, 23400, 26235, 29232, 32391, 35712, 39195, 42840, 46647, 50616, 54747, 59040, 63495, 68112, 72891, 77832, 82935, 88200, 93627, 99216, 104967, 110880, 116955, 123192
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OFFSET
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1,1
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COMMENTS
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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.: -9*x*(8 + 11*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) = 1/18 - Pi/(54*sqrt(3)).
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(27*sqrt(3)) - 1/18. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {72, 315, 720}, 50] (* Vincenzo Librandi, Feb 08 2012 *)
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PROG
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(Magma) I:=[72, 315, 720]; [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 08 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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