OEIS A000009: Partitions into distinct parts

Join us for a friendly tour of OEIS A000009, the sequence counting partitions of n into distinct parts. We’ll uncover the surprising bijection that makes partitions into distinct parts and partitions into odd parts the same in count, explore a staircase intuition, and see how Ramanujan theta functions and Euler transforms help unlock these patterns. Along the way, we’ll glimpse how this simple counting problem threads through combinatorics, number theory, and even mathematical physics. We’ll also peek at a tantalizing conjecture attributed to Sun: for all n > 7, the distinct-parts count does not divide the total number of partitions p(n). A compact, approachable look at a deceptively rich corner of math.

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