OEIS A000156: Representations of integers as the sum of 24 squares

In this episode we dive into OEIS A000156, the number of ways to express an integer as the sum of 24 squares. We unpack how these counts connect to deep ideas in number theory, including modular forms, Ramanujan’s tau function, and sums of divisors raised to the 11th power. We explore the generating function that ties the sequence to modular forms, and a recursive relation linking A000156 to the 12-squares sequence via A186690. Along the way we reflect on the broader significance of sums of squares in quadratic forms and their unexpected interconnections within the OEIS.

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