Exploring A000084: the number of unlabeled series-parallel networks with n edges. We’ll see how this simple counting problem ties into circuit topology, co-graphs, P4-free graphs, and equivalent resistances. Join us as we trace the math from McMahon’s yoke chains through Riordan, Shannon, Foster, Cameron, and the OEIS itself, uncovering how one sequence threads through combinatorics, graph theory, and network design.

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