What is the relevance of this comment to this post? Are you insinuating that the author did not come up with the right answer? That's odd here because the answers are actually verified in multiple ways (Sage code, looking up the numbers on OEIS).
Not at all, the post seems solid. Just fond memories of a combinatorics class in school. I like problems that are deceptively simple. Easy to get lured in to, then satisfying as layers of complexity are peeled back.