Felix Huber

Congruence Classes of Triangles in a Cubical Grid

For n >= 0, let G_n = {0,1,...,n}^3. This note studies the number a(n) of Euclidean congruence classes of nondegenerate triangles whose vertices lie in G_n, the three-dimensional analogue of the square-grid sequence A028419. An exact finite encoding is obtained from the 3*n*(n+1)/2 + 1 possible one-coordinate contribut...