  In this paper, we consider representations of integers as sums of at most
four distinct $m$-gonal numbers (allowing a fixed number of repeats of each
polygonal number occurring in the sum). We show that the number of such
representations with non-negative parameters (hence counting the number of
points in a regular $m$-gon) is asymptotically the same as $\frac{1}{16}$ times
the number of such representations with arbitrary integer parameters (often
called generalized polygonal numbers).
