A049021 Number of topologically distinct ways to dissect a rectangle into n rectangles.

1, 1, 2, 7, 23, 116, 683, 4866

Offset: 1

Author

Stuart E Anderson

Keywords

• nonn
• nice
• more

Comments

The data are from Mitchell, Steadman & Liggett (MSL). Combes gives terms 1, 2, 7, 23, 116, 685, 5124. Stesney reconstructed MSL's algorithm and got 2, 7, 23, 116, 685, 4899. For some higher n, MSL's algorithm is known not to be exhaustive [Steadman, pp. 39-40]. - Andrey Zabolotskiy, Sep 26 2023

References

• E. J. Sauda, Dissection generating algorithm (University of Louisiana), 1976.
• J. P. Steadman, Architectural Morphology, Pion Limited, London 1983, ISBN 0 85086 08605.

Links

• C. J. Bloch, Catalogue of small rectangular plans, Environment and Planning B, 6 (1979), 155-190. [Note: this paper is related to a similar but different sequence, see A375129.]
• C. J. Bloch and R. Krishnamurti, The Counting of Rectangular Dissections, Environ. Plann. B, 5 (1978), 207-214. [Note: this paper is related to a similar but different sequence, see A375129.]
• L. Combes, Packing Rectangles into Rectangular Arrangements, Environ. Plann. B, 3 (1976), 3-32.
• Peter Kagey, Example of the a(4)=7 dissections into n=4 pieces.
• W. J. Mitchell, J. P. Steadman and R. S. Liggett, Synthesis and optimization of small rectangular floor plans, Environment and Planning B, 1976 vol. 3, 37-70.
• Michael Stesney, Rematerializing Graphs: Learning Spatial Configuration, Master's Thesis, Carnegie Mellon University, 2021.

Crossrefs

Cf. A056814, A340984, A342141, A375129, A375130, A375131, A375132.