A087887 a(n) = 18n^3 + 6n^2.
0, 24, 168, 540, 1248, 2400, 4104, 6468, 9600, 13608, 18600, 24684, 31968, 40560, 50568, 62100, 75264, 90168, 106920, 125628, 146400, 169344, 194568, 222180, 252288, 285000, 320424, 358668, 399840, 444048, 491400, 542004, 595968, 653400, 714408, 779100, 847584
Offset: 0
Programs
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Mathematica
a[n_] := 18*n^3 + 6*n^2; Array[a, 50, 0] (* Amiram Eldar, Jan 10 2023 *)
Formula
O.g.f.: 12x(2+6x+x^2)/(-1+x)^4. a(n) = 12*A036659(n). - R. J. Mathar, Apr 07 2008
From Amiram Eldar, Jan 10 2023: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/36 + sqrt(3)*Pi/12 + 3*log(3)/4 - 3/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/72 - sqrt(3)*Pi/6 - log(2) + 3/2. (End)
Extensions
More terms from Ray Chandler, Nov 06 2003
Comments