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%I #11 Jan 10 2023 01:53:18
%S 0,24,168,540,1248,2400,4104,6468,9600,13608,18600,24684,31968,40560,
%T 50568,62100,75264,90168,106920,125628,146400,169344,194568,222180,
%U 252288,285000,320424,358668,399840,444048,491400,542004,595968,653400,714408,779100,847584
%N a(n) = 18n^3 + 6n^2.
%C Another parametric representation of the solutions of the Diophantine equation x^2 - y^2 =z^3 is (x,y,z) = (15n^3, 3n^3, 6n^2), thus getting a(n) = 18n^3 + 6n^2.
%F O.g.f.: 12x(2+6x+x^2)/(-1+x)^4. a(n)=12*A036659(n). - _R. J. Mathar_, Apr 07 2008
%F From _Amiram Eldar_, Jan 10 2023: (Start)
%F Sum_{n>=1} 1/a(n) = Pi^2/36 + sqrt(3)*Pi/12 + 3*log(3)/4 - 3/2.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/72 - sqrt(3)*Pi/6 - log(2) + 3/2. (End)
%t a[n_] := 18*n^3 + 6*n^2; Array[a, 50, 0] (* _Amiram Eldar_, Jan 10 2023 *)
%Y Cf. A085409, A085482.
%K easy,nonn
%O 0,2
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Oct 13 2003
%E More terms from _Ray Chandler_, Nov 06 2003
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