OEIS A000174: Five squares representations

Join us as we explore OEIS A000174, the count of representations of a nonnegative integer n as a sum of five squares. We discuss the counting convention used in the entry (order and signs) and how A000174(n) = A02635(n) + A02542(n): the four-squares representations plus the genuinely five-squares representations. We survey cross-references to related sums-of-squares sequences, the Mathematica snippet for generating terms, and classical references like E. Grosswald's Representations of Integers as Sums of Squares (page 84). We also touch on broader questions about how the number of representations grows with k and the inverse problem explored by A295160. A great primer for number theory fans and curious explorers alike.

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