  In this paper, we consider representations of integers as sums of generalized
heptagonal numbers with a prescribed number of repeats of each heptagonal
number appearing in the sum. In particular, we investigate the classification
of such sums which are universal, i.e., those that represent every positive
integer. We prove an explicit finite bound such that a given sum is universal
if and only if it represents positive integer up to the given bound.

Number Theory