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

0,3

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.

Sequence in context: A211071 A212135 A210569 * A341688 A341877 A005561

Adjacent sequences: A334578 A334579 A334580 * A334582 A334583 A334584

Keyword

nonn

Author

Peter Kagey, May 06 2020

Status

approved