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%I #21 Jun 25 2020 16:03:42
%S 6,40,126,288,550,936,1470,2176,3078,4200,5566,7200,9126,11368,13950,
%T 16896,20230,23976,28158,32800,37926,43560,49726,56448,63750,71656,
%U 80190,89376,99238,109800,121086,133120,145926,159528,173950,189216
%N a(n) = 4n^3 + 2n^2.
%C Yet another parametric representation of the solutions of the Diophantine equation x^2 - y^2 = z^3 is (3n^3, n^3, 2n^2). By taking the sum x+y+z we get a(n) = 4n^3 + 2n^2.
%C If Y is a 3-subset of an 2n-set X then, for n>=5, a(n-2) is the number of 5-subsets of X having at least two elements in common with Y. - _Milan Janjic_, Dec 16 2007
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 2*A099721(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: 2*x*(3+8*x+x^2)/(x-1)^4. [_R. J. Mathar_, Apr 20 2009]
%F a(n) = 2 * n * A014105(n). - _Richard R. Forberg_, Jun 16 2013
%t Table[4n^3+2n^2,{n,40}] (* _Harvey P. Dale_, Jun 12 2020 *)
%Y Cf. A085409, A087887.
%K nonn,easy
%O 1,1
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 09 2003
%E More terms from _Ray Chandler_, Feb 15 2004
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