The 32-Variable Octagonal Pillar is a variant of the 2 D or 3 D Cube Projected into Hexagon, with one orthoginal dimension added to make it a pillar. Please forgive my earlier mistake on the actual data, it is not 48 var, but I didn't notice until I tested the algebraic solution.

The summation is over an octagonal phased tiling, that it may tile with a Cubic Pascalloid of the same N.

and here is the cominatoric expression for the 48-Variable Octagonal Pillar, it's a doosie:

No Excel proof yet complete

And here is the algebraic paralel:

The geometry is still n-based, starting here at N=1. It is viewable here up to N=5

32^{1} = 32

32^{2} = 1,024

32^{3} = 32,768

32^{4} = 1,048,576

32^{5} = 33,554,432