OEIS A000072: Representations of numbers ≤ 2^n as x^2 + 4 y^n

A guided tour of A000072, the sequence counting how many positive integers up to 2^n can be written in the form x^2 + 4 y^n. We explore the number-theory and computational ideas behind the rule, including Gaussian integers, growth patterns, and PARI/GP code, and we touch on Sloan’s Handbook of Integer Sequences and the broader connections to discrete math and algorithms.

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