The expression (A-B+C-D+E-F)N is the expression for this new standardized operation of the Pascalloid algorithm in this case, where the coefficients actually combine algebraically with the terms, and are quite naturally expressed as separate polynomials added in the output, following this algebraic expansion:

Hexagonal number structure with paralel algebraic equation

Hexagonal ring of variables, 3+, 3-, with the two center variables aligned & canceled out.

Though it took years of thinking the algebra solution impossible, this algorithm was designed only to match the coefficients of this polarized equation, and does so nicely. Its non-polar cousin geometry isn't "Hexagon A" (which yet has no equation), instead this is a polar version of the 'Projected 8-var Hexagon from Cube', though here the cube being polar causes the direct center terms to cancel at N=1, simplifying the algorithm into its amazing polar form. If I were asked why the algebraic equation works, I would say "because I tested it". If asked "what is it for?", I would say "energetic, moving or material vibrations, just like all other polar algebra equations (as we know with Binomials, (A-B)^N and everything somewhat based on it).". There are many of these 'cousins' that are not posted yet, but most of them can easily be guessed, and proven, as long as you have a way to test them.

N = 0
N = 1
N = 2
N = 3
N = 4
N = 5
N = 6
N = 7
N = 8
N = 9
N = 10
N = 11
N = 12
N = 13
N = 14
N = 15
N = 16
N = 17
N = 18
N = 19
N = 20
N = 21


This algorithm ideally involves minimal creativity, as it mimes perfectly the coefficients of the expansions of the algebraic equation given at the top. The sum of each N+1 iteration, even the whole out to ∞ becomes a usual "convergent sum". If the data was examined as a whole that way, this convergent sum is zero, has always been zero whenever I checked, except for at N = 0 where the grand total was '1', and thus the whole structure as a traditional summation can safely be assumed to be a grand total of '1' when all results of N are summed 0 through N = ∞.