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%I #24 Aug 28 2020 02:01:02
%S 0,0,4,24,84,224,516,1068,2016,3528,5832,9256,14208,21180,30728,43488,
%T 60192,81660,108828,142764,184708,236088,298476,373652,463524,570228,
%U 696012,843312,1014720,1213096,1441512,1703352,2002196,2341848,2726400,3160272,3648180
%N Number of ways to choose 3 points that form an equilateral triangle from the A000292(n) points in a regular tetrahedral grid of side length n.
%C a(n) >= 4 * A269747(n).
%C a(n) >= 4 * A000389(n+3) = A210569(n+2).
%C a(n) >= 4 * (n-1) + 4 * a(n-1) - 6 * a(n-2) + 4 * a(n-3) - a(n-4) for n >= 4.
%H Peter Kagey, <a href="/A334581/b334581.txt">Table of n, a(n) for n = 0..1000</a> (Computed via Anders Kaseorg's program in the Stack Exchange link.)
%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/204419/53884">Triangles in a tetrahedron</a>
%Y Cf. A000292, A000389, A210569.
%Y Cf. A000332 (equilateral triangles in triangular grid), A269747 (regular tetrahedra in a tetrahedral grid), A102698 (equilateral triangles in cube), A103158 (regular tetrahedra in cube).
%Y Cf. A077435, A085582, A187452, A189412-A189418, A271910.
%K nonn
%O 0,3
%A _Peter Kagey_, May 06 2020
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