A348351 Number of permutations avoiding the patterns 2-41-3, 3-14-2, 2-14-3, and 3-41-2.

1, 1, 2, 6, 20, 72, 274, 1088, 4470, 18884, 81652, 360054, 1614618, 7346688, 33856008, 157777908, 742637416

Offset

0,3

Comments

Also the number of one-sided rectangulations.

References

L. J. Leifheit, Combinatorial Properties of Rectangulations, Master's thesis, Technische Universität Berlin, 2021.

Links

Table of n, a(n) for n=0..16.

A. Asinowski, G. Barequet, M. Bousquet-Mélou, T. Mansour, and R. Y. Pinter, Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations, Electronic Journal of Combinatorics 20(2), 2013.

Andrei Asinowski, Jean Cardinal, Stefan Felsner, and Éric Fusy, Combinatorics of rectangulations: Old and new bijections, arXiv:2402.01483 [math.CO], 2023. See p. 30.

D. Eppstein, E. Mumford, B. Speckmann, and K. Verbeek, Area-Universal Rectangular Layouts, arXiv:0901.3924 [cs.CG], 2009.

A. Merino and T. Mütze, Combinatorial generation via permutation languages. III. Rectangulations, arXiv:2103.09333 [math.CO], 2021.

M. Scheucher, L.J. Leifheit's python program for enumeration.

The Combinatorial Object Server, Rectangulation Generator.

Crossrefs

Cf. A001181, A006318, A078482.

Sequence in context: A272485 A122737 A338184 * A150134 A059279 A154381

Adjacent sequences: A348348 A348349 A348350 * A348352 A348353 A348354

Keyword

nonn,more

Author

Manfred Scheucher, Oct 20 2021

Extensions

Name corrected by Manfred Scheucher, May 24 2023

a(0)=1 prepended by Alois P. Heinz, Feb 05 2024

Status

approved