OEIS A000270: Discordant permutations

We dive into OEIS A000270, the “Discordant permutations” sequence. We’ll unpack what it counts—permutations of {1, …, n+1} that are discordant with two reference permutations (the identity and a fixed-point plus an n-cycle)—and why this setup connects to the famous menage numbers (A000179) via a simple recurrence. We’ll also touch on the historical quirks, like the A0/A1 start values and why OEIS keeps a 0,1 entry to echo an old paper, plus a nod to the generating function and what these links reveal about the hidden structure in permutations and the role of OEIS as both math resource and historical archive.

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