OEIS A000214: Essential Boolean function types under affine symmetry AGN2

We explore how A000214 counts the equivalence classes of n-variable Boolean functions under the action of the binary affine group AGN2. An affine transformation over GF(2) reshapes inputs via invertible linear maps and translations, collapsing tens of thousands of functions into a small set of fundamentally different types (3 for n=1, 5 for n=2, 10 for n=3, 32 for n=4, 382 for n=5). We explain why this symmetry-based classification matters for circuit design and cryptography, and touch on the combinatorial machinery (Burnside's lemma, Pólya enumeration) used to compute terms, plus connections to related sequences such as self-dual Boolean functions.

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