A342141 The number of generic rectangulations with n rectangles.

1, 2, 6, 24, 116, 642, 3938, 26194, 186042, 1395008, 10948768, 89346128, 754062288, 6553942722, 58457558394, 533530004810, 4970471875914, 47169234466788, 455170730152340, 4459456443328824, 44300299824885392, 445703524836260400, 4536891586511660256, 46682404846719083048, 485158560873624409904, 5089092437784870584576, 53845049871942333501408

Offset: 1

Author

Peter Kagey, Mar 01 2021

Keywords

• nonn

Comments

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

Links

• Andrei Asinowski, Jean Cardinal, Stefan Felsner, and Éric Fusy, Combinatorics of rectangulations: Old and new bijections, arXiv:2402.01483 [math.CO], 2023. See p. 11 and p. 27.
• Jean Cardinal and Vincent Pilaud, Rectangulotopes, arXiv:2404.17349 [math.CO], 2024. See p. 18.
• CombOS - Combinatorial Object Server, Generate generic rectangulations
• Éric Fusy, Erkan Narmanli, and Gilles Schaeffer, On the enumeration of plane bipolar posets and transversal structures, arXiv:2105.06955 [math.CO], 2021-2023. See p. 16.
• Arturo Merino and Torsten Mütze, Combinatorial generation via permutation languages. III. Rectangulations, arXiv:2103.09333 [math.CO], 2021.
• Nathan Reading, Generic rectangulations, arXiv:1105.3093 [math.CO], 2011-2012.

Crossrefs

Cf. A049021, A340984.