A375913 Number of strong (=generic) guillotine rectangulations with n rectangles.

1, 2, 6, 24, 114, 606, 3494, 21434, 138100, 926008, 6418576, 45755516, 334117246, 2491317430, 18919957430, 146034939362, 1143606856808, 9072734766636, 72827462660824, 590852491725920, 4840436813758832, 40009072880216344, 333419662183186932, 2799687668599080296

Offset: 1

Author

Andrei Asinowski, Sep 02 2024

Keywords

• nonn

Comments

Equivalently: The number of strong rectangulations with n rectangles that avoid two windmill patterns.

Links

• Andrei Asinowski, Jean Cardinal, Stefan Felsner, and Éric Fusy, Combinatorics of rectangulations: Old and new bijections, arXiv:2402.01483 [math.CO], 2024, page 37.
• Arturo Merino and Torsten Mütze, Combinatorial generation via permutation languages. III. Rectangulations, Discrete Comput. Geom., 70(1):51-122, 2023. Page 99, Table 3, entry "12".

Crossrefs

Cf. A342141 (number of strong (=generic) rectangulations).

Cf. A001181 (Baxter numbers: number of weak (=diagonal) rectangulations).

Cf. A006318 (Schröder numbers: number of weak (=diagonal) guillotine rectangulations).

Formula

A 5-variate recurrence is given in the paper Asinowski, Cardinal, Felsner, and Fusy.