Hardy-Weinberg principle
I can't think of a more succinct way to phrase it than the explanation in your post.

&quot;...the genotype frequencies of the next generation depend only on the
allele frequencies of the current generation...&quot;

The genotype frequencies still do depend on the initial generation, they just depend on the allele frequencies of the previous generation, not the genotype frequencies. For example, an initial generation consisting of only (XX) and (xx) genotypes will produce F1 offspring with (XX), (Xx), and (xx) genotypes through random mating. Since the (Xx) genotype frequency was 0% in the initial generation, and &gt;0% in the subsequent generations, it can't be equal that of the initial generation. But it will still be a function of the relative frequencies of the two alleles in the population, (X) and (x).