OEIS A000075: Representations by the quadratic form 2x^2 + 3y^2 up to 2^n

We explore A000075, the count of integers ≤ 2^n that can be written as 2x^2 + 3y^2 with integers x and y. For n = 3, there are four such integers: 2, 3, 5, and 8. Along the way we connect this to the theory of quadratic forms, note its appearances in Sloan’s Handbook and Encyclopedia of Integer Sequences, and show how the OEIS provides PARI and Python code to generate the sequence, with links to related sequences and important offset conventions.

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