%I #18 Mar 09 2019 15:58:25
%S 0,16,111,439,1305,3240,7091,14126,26154,45660,75955,121341,187291,
%T 280644,409815,585020,818516,1124856,1521159,2027395,2666685,3465616,
%U 4454571,5668074,7145150,8929700,11070891,13623561,16648639,20213580,24392815,29268216,34929576
%N Number of ways to choose 3 points in an n X n X n triangular grid so that they do not form a 2 X 2 X 2 triangle.
%H Heinrich Ludwig, <a href="/A234250/b234250.txt">Table of n, a(n) for n = 2..999</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1)
%F a(n) = (n - 1)*(n - 2)*(n^4 + 6*n^3 + 13*n^2 + 16*n - 24)/48.
%F G.f.: x^3*(x^4-3*x^3+2*x^2+x-16) / (x-1)^7. - _Colin Barker_, Feb 05 2014
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,16,111,439,1305,3240,7091},40] (* _Harvey P. Dale_, Mar 09 2019 *)
%o (PARI) Vec(x^3*(x^4-3*x^3+2*x^2+x-16)/(x-1)^7 + O(x^100)) \\ _Colin Barker_, Feb 05 2014
%K nonn,easy
%O 2,2
%A _Heinrich Ludwig_, Feb 04 2014