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A140673
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a(n) = 3*n*(n + 5)/2.
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13
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0, 9, 21, 36, 54, 75, 99, 126, 156, 189, 225, 264, 306, 351, 399, 450, 504, 561, 621, 684, 750, 819, 891, 966, 1044, 1125, 1209, 1296, 1386, 1479, 1575, 1674, 1776, 1881, 1989, 2100, 2214, 2331, 2451, 2574, 2700, 2829, 2961, 3096
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = A055998(n)*3 = (3*n^2 + 15*n)/2 = n*(3*n + 15)/2.
E.g.f.: (1/2)*(3*x^2 + 18*x)*exp(x). - G. C. Greubel, Jul 17 2017
Sum_{n>=1} 1/a(n) = 137/450.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/15 - 47/450. (End)
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MATHEMATICA
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Table[Sum[i + n - 3, {i, 6, n}], {n, 5, 52}] (* Zerinvary Lajos, Jul 11 2009 *)
LinearRecurrence[{3, -3, 1}, {0, 9, 21}, 50] (* Harvey P. Dale, Jul 20 2023 *)
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PROG
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(PARI) concat(0, Vec(3*x*(3 - 2*x)/(1 - x)^3 + O(x^100))) \\ Michel Marcus, Apr 20 2015
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CROSSREFS
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The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.
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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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