A334581 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.

0, 0, 4, 24, 84, 224, 516, 1068, 2016, 3528, 5832, 9256, 14208, 21180, 30728, 43488, 60192, 81660, 108828, 142764, 184708, 236088, 298476, 373652, 463524, 570228, 696012, 843312, 1014720, 1213096, 1441512, 1703352, 2002196, 2341848, 2726400, 3160272, 3648180

Offset: 0

Author

Peter Kagey, May 06 2020

Keywords

• nonn

Comments

a(n) >= 4 * A269747(n).

a(n) >= 4 * A000389(n+3) = A210569(n+2).

a(n) >= 4 * (n-1) + 4 * a(n-1) - 6 * a(n-2) + 4 * a(n-3) - a(n-4) for n >= 4.

Links

• Peter Kagey, Table of n, a(n) for n = 0..1000 (Computed via Anders Kaseorg's program in the Stack Exchange link.)
• Code Golf Stack Exchange, Triangles in a tetrahedron

Crossrefs

Cf. A000292, A000389, A210569.

Cf. A000332 (equilateral triangles in triangular grid), A269747 (regular tetrahedra in a tetrahedral grid), A102698 (equilateral triangles in cube), A103158 (regular tetrahedra in cube).

Cf. A077435, A085582, A187452, A189412-A189418, A271910.