Tetrahedral Pascalloids, the most basic Three-dimensional pascalloid, can be expressed with the same algebra as the Two-dimensional Square Pascalloid in one form, that being ((A+B+C+D))N, and the terms will hold accurate in this case (of the Tetrahedral).

        N!       
X!Y!Z! (N-X-Y-Z)!

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This has been found to be the Geometric Combinatorics equation for the Tetrahedral Pascalloid.

The secrets to programming this app in Flash 8 were mainly to delete three elements of the Cubic Pascalloid, and then provide a transformation (stretching far corners of a cube) of the grid-like co-ordinate system until it was perfectly Tetrahedral (co-ordintates) in scope.

Three views of the Tetrahedral Pascalloid at N=1, sum total = 41 = 4
Three views of the Tetrahedral Pascalloid at N=2, sum total = 42 = 16
Three views of the Tetrahedral Pascalloid at N=3, sum total = 43 = 64
Three views of the Tetrahedral Pascalloid at N=4, sum total = 44 = 256
Three views of the Tetrahedral Pascalloid at N=5, sum total = 45 = 1,024
Three views of the Tetrahedral Pascalloid at N=6, sum total = 46 = 4,096
Three views of the Tetrahedral Pascalloid at N=7, sum total = 47 = 16,384
Three views of the Tetrahedral Pascalloid at N=8, sum total = 48 = 65,536