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%I #31 Sep 27 2023 04:33:58
%S 1,1,2,7,23,116,683,4866
%N Number of topologically distinct ways to dissect a rectangle into n rectangles.
%C 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
%D E. J. Sauda, Dissection generating algorithm (University of Louisiana), 1976.
%D J. P. Steadman, Architectural Morphology, Pion Limited, London 1983, ISBN 0 85086 08605.
%H C. J. Bloch, <a href="https://doi.org/10.1068/b060155">Catalogue of small rectangular plans</a>, Environment and Planning B, 6 (1979), 155-190.
%H C. J. Bloch and R. Krishnamurti, <a href="https://doi.org/10.1068/b050207">The Counting of Rectangular Dissections</a>, Environ. Plann. B, 5 (1978), 207-214.
%H L. Combes, <a href="https://doi.org/10.1068/b030003">Packing Rectangles into Rectangular Arrangements</a>, Environ. Plann. B, 3 (1976), 3-32.
%H Peter Kagey, <a href="/A049021/a049021.png">Example of the a(4)=7 dissections into n=4 pieces</a>.
%H W. J. Mitchell, J. P. Steadman and R. S. Liggett, <a href="https://doi.org/10.1068/b030037">Synthesis and optimization of small rectangular floor plans</a>, Environment and Planning B, 1976 vol. 3.
%H Michael Stesney, <a href="https://kilthub.cmu.edu/articles/thesis/Rematerializing_Graphs_Learning_Spatial_Configuration/21391395/1">Rematerializing Graphs: Learning Spatial Configuration</a>, Master's Thesis, Carnegie Mellon University, 2021.
%Y Cf. A056814.
%K nonn,nice,more
%O 1,3
%A _Stuart E Anderson_
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