Deep Dive: A000006 — Squares, Boundaries, and the OEIS

We explore A000006 from the OEIS, decoding the quadratic form 4x^2 + 4xy + 5y^2. Using Bert Dobbeler's completing-the-square trick to rewrite it as (2x + y)^2 + 4y^2, we count how many integers are representable up to 2^n, illustrated with n = 4. Along the way we glimpse geometry, number theory, and the collaborative spirit that powers the OEIS.

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