cp's OEIS Frontend

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

%I A049021 #41 Aug 01 2024 01:19:26
%S A049021 1,1,2,7,23,116,683,4866
%N A049021 Number of topologically distinct ways to dissect a rectangle into n rectangles.
%C A049021 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
%D A049021 E. J. Sauda, Dissection generating algorithm (University of Louisiana), 1976.
%D A049021 J. P. Steadman, Architectural Morphology, Pion Limited, London 1983, ISBN 0 85086 08605.
%H A049021 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. [Note: this paper is related to a similar but different sequence, see A375129.]
%H A049021 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. [Note: this paper is related to a similar but different sequence, see A375129.]
%H A049021 L. Combes, <a href="https://doi.org/10.1068/b030003">Packing Rectangles into Rectangular Arrangements</a>, Environ. Plann. B, 3 (1976), 3-32.
%H A049021 Peter Kagey, <a href="/A049021/a049021.png">Example of the a(4)=7 dissections into n=4 pieces</a>.
%H A049021 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, 37-70.
%H A049021 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 A049021 Cf. A056814, A340984, A342141, A375129, A375130, A375131, A375132.
%K A049021 nonn,nice,more
%O A049021 1,3
%A A049021 _Stuart E Anderson_