%I #61 Feb 05 2024 09:25:31
%S 1,1,2,6,20,72,274,1088,4470,18884,81652,360054,1614618,7346688,
%T 33856008,157777908,742637416
%N Number of permutations avoiding the patterns 2-41-3, 3-14-2, 2-14-3, and 3-41-2.
%C Also the number of one-sided rectangulations.
%D L. J. Leifheit, Combinatorial Properties of Rectangulations, Master's thesis, Technische Universität Berlin, 2021.
%H A. Asinowski, G. Barequet, M. Bousquet-Mélou, T. Mansour, and R. Y. Pinter, <a href="https://doi.org/10.37236/2607">Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations</a>, Electronic Journal of Combinatorics 20(2), 2013.
%H Andrei Asinowski, Jean Cardinal, Stefan Felsner, and Éric Fusy, <a href="https://arxiv.org/abs/2402.01483">Combinatorics of rectangulations: Old and new bijections</a>, arXiv:2402.01483 [math.CO], 2023. See p. 30.
%H D. Eppstein, E. Mumford, B. Speckmann, and K. Verbeek, <a href="https://arxiv.org/abs/0901.3924">Area-Universal Rectangular Layouts</a>, arXiv:0901.3924 [cs.CG], 2009.
%H A. Merino and T. Mütze, <a href="https://arxiv.org/abs/2103.09333">Combinatorial generation via permutation languages. III. Rectangulations</a>, arXiv:2103.09333 [math.CO], 2021.
%H M. Scheucher, <a href="/A348351/a348351.py.txt">L.J. Leifheit's python program for enumeration</a>.
%H The Combinatorial Object Server, <a href="http://combos.org/rect">Rectangulation Generator</a>.
%Y Cf. A001181, A006318, A078482.
%K nonn,more
%O 0,3
%A _Manfred Scheucher_, Oct 20 2021
%E Name corrected by _Manfred Scheucher_, May 24 2023
%E a(0)=1 prepended by _Alois P. Heinz_, Feb 05 2024