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A157888
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a(n) = 81*n^2 + 9.
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3
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90, 333, 738, 1305, 2034, 2925, 3978, 5193, 6570, 8109, 9810, 11673, 13698, 15885, 18234, 20745, 23418, 26253, 29250, 32409, 35730, 39213, 42858, 46665, 50634, 54765, 59058, 63513, 68130, 72909, 77850, 82953, 88218, 93645, 99234, 104985, 110898, 116973, 123210
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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: x*(90 + 63*x + 9*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=1} 1/a(n) = (coth(Pi/3)*Pi/3 - 1)/18.
Sum_{n>=1} (-1)^(n+1)/a(n) = (1 - cosech(Pi/3)*Pi/3)/18. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {90, 333, 738}, 40] (* Vincenzo Librandi, Feb 05 2012 *)
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PROG
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(Magma) I:=[90, 333, 738]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 05 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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