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A334581
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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.
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5
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Peter Kagey, May 06 2020
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STATUS
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approved
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