cp's OEIS Frontend

A342141 The number of generic rectangulations with n rectangles.

%I A342141 #36 Sep 03 2024 01:02:08
%S A342141 1,2,6,24,116,642,3938,26194,186042,1395008,10948768,89346128,
%T A342141 754062288,6553942722,58457558394,533530004810,4970471875914,
%U A342141 47169234466788,455170730152340,4459456443328824,44300299824885392,445703524836260400,4536891586511660256,46682404846719083048,485158560873624409904,5089092437784870584576,53845049871942333501408
%N A342141 The number of generic rectangulations with n rectangles.
%C A342141 a(n) is also the number of two-clumped permutations of size n. Two-clumped permutations are (3-51-2-4, 3-51-4-2, 2-4-51-3, 4-2-51-3)-avoiding permutations. This class was introduced in the paper by Reading, where a bijection to generic rectangulations was also given. - _Andrei Asinowski_, Sep 02 2024
%H A342141 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. 11 and p. 27.
%H A342141 Jean Cardinal and Vincent Pilaud, <a href="https://arxiv.org/abs/2404.17349">Rectangulotopes</a>, arXiv:2404.17349 [math.CO], 2024. See p. 18.
%H A342141 CombOS - Combinatorial Object Server, <a href="http://combos.org/rect">Generate generic rectangulations</a>
%H A342141 Éric Fusy, Erkan Narmanli, and Gilles Schaeffer, <a href="https://arxiv.org/abs/2105.06955">On the enumeration of plane bipolar posets and transversal structures</a>, arXiv:2105.06955 [math.CO], 2021-2023. See p. 16.
%H A342141 Arturo Merino and Torsten Mütze, <a href="https://arxiv.org/abs/2103.09333">Combinatorial generation via permutation languages. III. Rectangulations</a>, arXiv:2103.09333 [math.CO], 2021.
%H A342141 Nathan Reading, <a href="https://arxiv.org/abs/1105.3093">Generic rectangulations</a>, arXiv:1105.3093 [math.CO], 2011-2012.
%Y A342141 Cf. A049021, A340984.
%K A342141 nonn
%O A342141 1,2
%A A342141 _Peter Kagey_, Mar 01 2021