2 problems

Let $x$ and $y$ be nonnegative integers, and consider nonnegative integers of the form … The values in OEIS A051221 that are at most $2000$ are known for $x\leq 7$. Completeness co…

For $n\ge0$, let $\chi(\mathcal S)$ be the number of distinct parts occurring in a set of partitions $\mathcal S$, and let $\tau(\mathcal S)$ count parts with multiplicity. Let…