OEIS A000161: Partitions of n into two squares

We explore A000161, the number of ways to write n as a sum of two squares, counting unordered pairs of nonnegative integers (zero allowed). We unpack what 'partition' means in this context, why zeros appear, and how this links to similar sublattices of the square lattice. We’ll connect to the larger family of 'pk' partitions (k squares) like A010052 and A025426, examine the divisor- and modulo-4 based formulas, walk through the example n = 25 (A25 = 2), and look at practical code for generating terms. We'll also point to key references and the geometric viewpoint that ties representations of numbers to lattice patterns, including work by Conway–Rains–Sloane and Grosswald for deeper exploration.

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