We explain A00282—the number of inequivalent N-state, two-input, two-output connected automata up to input permutation. We'll unpack what N-state, two inputs/outputs, connected, and inequivalent mean, show why the counts explode (3, 70, 3,783, ...), and sketch the story from Harrison's 1965 census through Theorems 6.2 and 7.2 with the inverse Wehler transform to isolate the connected case—and why these counts matter for understanding the limits and structure of computation.

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