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A178977
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a(n) = (3*n+2)*(3*n+5)/2.
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3
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5, 20, 44, 77, 119, 170, 230, 299, 377, 464, 560, 665, 779, 902, 1034, 1175, 1325, 1484, 1652, 1829, 2015, 2210, 2414, 2627, 2849, 3080, 3320, 3569, 3827, 4094, 4370, 4655, 4949, 5252, 5564, 5885, 6215, 6554, 6902, 7259, 7625, 8000, 8384, 8777, 9179
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(n-1)+6+9*n.
G.f.: (-5-5*x+x^2)/(x-1)^3. [Adapted to the offset by Bruno Berselli, Apr 14 2011]
Sum_{n>=0} 1/a(n) = 1/3.
Sum_{n>=0} (-1)^n/a(n) = 4*Pi/(9*sqrt(3)) - 1/3 - 4*log(2)/9. (End)
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MAPLE
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MATHEMATICA
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f[n_] := (3 n + 2) (3 n + 5)/2; Array[f, 45, 0]
LinearRecurrence[{3, -3, 1}, {5, 20, 44}, 50] (* Harvey P. Dale, Apr 19 2013 *)
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PROG
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(Magma) [n*(n+3)/2: n in [2..135 by 3]]; // Bruno Berselli, Apr 14 2011
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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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