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

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

Offset

1,3

Comments

The data is from Mitchell, Steadman & Liggett (MSL). Steadman gives terms 1, 1, 2, 7, 23, 119 on p. 31, and terms 24, 126, 815, 6465 for n=5..8 on p. 59, citing Bloch & Krishnamurti. The latter numbers are supported by Bloch's catalog; in particular, for n = 5 the dissection labeled "Grating (3,3), 5 fronts, 0401, C_2" is apparently missing from MSL's list, possibly because they don't distinguish it from "Grating (2,3), 5 fronts, 0401, K_4". Combes gives terms 1, 2, 7, 23, 116, 685, 5124. Stesney reconstructed MSL's algorithm and got 2, 7, 23, 116, 685, 4899. The differences in terms are possibly explained by subtle differences in definitions, or by errors, or both. - 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

Table of n, a(n) for n=1..8.

C. J. Bloch, Catalogue of small rectangular plans, Environment and Planning B, 6 (1979), 155-190.

C. J. Bloch and R. Krishnamurti, The Counting of Rectangular Dissections, Environ. Plann. B, 5 (1978), 207-214.

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.

Michael Stesney, Rematerializing Graphs: Learning Spatial Configuration, Master's Thesis, Carnegie Mellon University, 2021.

Crossrefs

Cf. A056814.

Sequence in context: A038119 A006986 A000903 * A345871 A332802 A002494

Adjacent sequences: A049018 A049019 A049020 * A049022 A049023 A049024

Keyword

nonn,nice,more

Author

Stuart E Anderson

Status

approved