OEIS A000231: Number of inequivalent Boolean functions under input complementation and output negation

We explore A000231, the count of inequivalent Boolean functions of n variables under the complementing group—the symmetries obtained by flipping any subset of inputs and possibly flipping the overall output. We introduce what a Boolean function is, what the group action means, and why two functions are in the same class if you can obtain one from the other by input negations and an output negation. We then discuss how this symmetry reduces the astronomical total 2^{2^n} functions to a much smaller sequence of equivalence classes, and how counting under symmetry brings in tools like Burnside's lemma and orbit-stabilizer ideas. Finally we connect this counting perspective to number theory, illustrating how group actions, modular reasoning, and symmetry arise in counting problems across math, not just logic design.

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