A348351 -id:A348351 - cp's OEIS frontend

A375923 Number of permutations of size n which are both two-clumped and co-two-clumped.

1, 1, 2, 6, 24, 112, 582, 3272, 19550, 122628, 800392, 5400342, 37475474, 266412680, 1934033968, 14300538652, 107471798112, 819442325086, 6329551390064, 49465665347580, 390692732060804, 3115700976866356, 25067250869113332, 203317147838575616, 1661425311693158000

Offset: 0

Andrei Asinowski, Sep 02 2024

nonn

Two-clumped permutations are (3-51-2-4, 3-51-4-2, 2-4-51-3, 4-2-51-3)-avoiding permutations. Co-two-clumped permutations are (3-15-2-4, 3-15-4-2, 2-4-15-3, 4-2-15-3)-avoiding permutations. Thus, this sequence enumerates permutations that avoid all these eight patterns.

a(n) is also the number of strong (=generic) rectangulations of size n whose strong poset is totally ordered.

Andrei Asinowski, Jean Cardinal, Stefan Felsner, and Éric Fusy, Combinatorics of rectangulations: Old and new bijections, arXiv:2402.01483 [math.CO], 2024, page 29.

Cf. A342141 (number of two-clumped permutations).
Cf. A001181 (Baxter numbers: number of (twisted-)Baxter permutations).
Cf. A348351 (number of permutations which are both twisted-Baxter and co-twisted-Baxter).

cp's OEIS Frontend

A375923 Number of permutations of size n which are both two-clumped and co-two-clumped.

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