A375129 -id:A375129 - cp's OEIS frontend

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

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

Offset: 1

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

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

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.

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

A375130 Number of nonaligned dissections of a rectangle into n rectangles.

Original entry on oeis.org

1, 1, 2, 7, 23, 119, 735, 5527, 46204, 423724

Offset: 1

Andrey Zabolotskiy, Jul 31 2024

Among the dissections counted by A375129, this sequence counts only those without "alignments". See A375129 for the details.

J. P. Steadman, Architectural Morphology, Pion Limited, 1983. See Table 5.2 on p. 59.

Cf. A049021, A340984, A342141, A375129, A375131, A375132.

A375131 Number of trivalent dissections of a rectangle into n rectangles.

Original entry on oeis.org

1, 1, 2, 6, 22, 108, 668, 5026, 43005, 389803

Offset: 1

Andrey Zabolotskiy, Jul 31 2024

Among the dissections counted by A375129, this sequence counts only those without 4-way junctions. See A375129 for the details.

J. P. Steadman, Architectural Morphology, Pion Limited, 1983. See Table 5.2 on p. 59.

Cf. A049021, A340984, A342141, A375129, A375130, A375132.

A375132 Number of nonaligned trivalent dissections of a rectangle into n rectangles.

Original entry on oeis.org

1, 1, 2, 6, 21, 101, 591, 4168, 32754, 282605

Offset: 1

Andrey Zabolotskiy, Jul 31 2024

J. P. Steadman, Architectural Morphology, Pion Limited, 1983. See Table 5.2 on p. 59.

Cf. A049021, A340984, A342141, A375129, A375130, A375131.

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

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A375130 Number of nonaligned dissections of a rectangle into n rectangles.

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A375131 Number of trivalent dissections of a rectangle into n rectangles.

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A375132 Number of nonaligned trivalent dissections of a rectangle into n rectangles.

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