A269747 Number of regular tetrahedra in an n-node-per-edge tetrahedral grid.

0, 0, 1, 5, 16, 39, 80, 155, 281, 476, 760, 1154, 1686, 2394, 3331, 4551, 6110, 8065, 10486, 13461, 17079, 21430, 26606, 32726, 39928, 48360, 58183, 69573, 82708, 97767, 114930, 134387, 156329, 180960, 208506, 239230, 273444, 311486, 353709, 400467, 452136, 509093, 571716, 640393, 715537

Offset

0,4

Comments

Number of ways to choose 4 points forming a regular tetrahedron out of the binomial(n+2,3) points in a regular tetrahedral grid.

The tetrahedra defined by the four points may have any orientation.

Similar to A216173, which differs from the present sequence in a mysterious way.

Links

Table of n, a(n) for n=0..44.

Formula

It would be nice to have a g.f. - N. J. A. Sloane, Mar 21 2016

Crossrefs

Cf. A000332 (2-D version), A216173, A270805, A270806.

Sequence in context: A082190 A155965 A216173 * A011863 A027085 A099452

Adjacent sequences: A269744 A269745 A269746 * A269748 A269749 A269750

Keyword

nonn

Author

Warren D. Smith, Mar 21 2016; more terms Mar 23 2016

Extensions

a(21) changed from 24130 to 21430 by Anthony Guttmann, Mar 07 2023

Status

approved