OEIS A000337: From binary zeros to polyominoes and primes

In this Deep Dive, we explore A000337, a small-seeming sequence that threads through binary arithmetic, geometry, and number theory. We'll trace how its simple definition links to counting zeros and bits in binary lists, to directed column-convex polyominoes, and to the genus of cube graphs. Along the way we’ll encounter prime and semiprime patterns noted by researchers, a neat generating function and a linear recurrence, and a combinatorial interpretation as sums of subset maxima. Join us as we uncover how one formula can map across disparate areas of math—and consider what other seemingly plain sequences in the OEIS are quietly weaving together multiple fields.

Note:  This podcast was AI-generated, and sometimes AI can make mistakes.  Please double-check any critical information.

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