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

321 = 32
322 = 1,024
323 = 32,768
324 = 1,048,576
325 = 33,554,432