A334891 Number of ways to choose 4 points that form a square from the A000292(n) points in a regular tetrahedral grid where each side has n vertices.

0, 0, 3, 12, 36, 84, 174, 336, 612, 1044, 1701

Offset

0,3

Comments

a(n) >= 3*A001752(n-2).

Links

Table of n, a(n) for n=0..10.

Example

For n = 4, three of the a(4) = 36 squares are (in barycentric coordinates)
  {(0,2,1,1),(1,1,0,2),(1,1,2,0),(2,0,1,1)},
  {(0,0,2,2),(0,2,0,2),(2,0,2,0),(2,2,0,0)}, and
  {(0,0,1,3),(0,1,0,3),(1,0,1,2),(1,1,0,2)}.
The other squares can be derived from these by translations or symmetries of the tetrahedron.

Crossrefs

Cf. A000292, A001752.

Cf. A334581 (equilateral triangle), A334881 (cubic grid).

Sequence in context: A135190 A101069 A225259 * A242526 A167667 A292291

Adjacent sequences: A334888 A334889 A334890 * A334892 A334893 A334894

Keyword

nonn,more

Author

Peter Kagey, May 14 2020

Status

approved