OEIS A000271: Sums of Ménage Numbers

From the classic round-table ménage problem, we tour the world of integer sequences that sums of ménage numbers unlock. We explain how the circular counts tie to linear seatings, Chevelev’s insight that the circle counts arise as scaled linear counts, and the neat four-term recurrence that builds n from n−1, n−2, and n−3. Along the way we glimpse curtains of graph theory (crown graphs), permanents, and a surprising knot-theory connection, illustrating how a simple seating puzzle reveals a rich web of combinatorial structure.

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