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A334891 Number of ways to choose 4 points that form an square from the A000292(n) points in a regular tetrahedral grid where each side has n vertices. 0
0, 0, 3, 12, 36, 84, 174, 336, 612, 1044, 1701 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 19:53 EDT 2022. Contains 354885 sequences. (Running on oeis4.)