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

Author

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

Keywords

• nonn

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.

Crossrefs

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

Formula

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

Extensions

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