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 = 4^{1} = 4

Three views of the Tetrahedral Pascalloid at N=2,
sum total = 4^{2} = 16

Three views of the Tetrahedral Pascalloid at N=3,
sum total = 4^{3} = 64

Three views of the Tetrahedral Pascalloid at N=4,
sum total = 4^{4} = 256

Three views of the Tetrahedral Pascalloid at N=5,
sum total = 4^{5} = 1,024

Three views of the Tetrahedral Pascalloid at N=6,
sum total = 4^{6} = 4,096

Three views of the Tetrahedral Pascalloid at N=7,
sum total = 4^{7} = 16,384

Three views of the Tetrahedral Pascalloid at N=8,
sum total = 4^{8} = 65,536