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A108066
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Number of distinct ways to dissect a square into n rectangles of equal area.
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6
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OFFSET
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1,3
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COMMENTS
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"Distinct" here means that dissections differing only by a rotation and/or reflection are not counted as different (see A189243).
The first time the pieces can be made to all have different shapes (but the same area) is at n=7 - see Descartes (1971) and the illustration; also Wells, Weisstein. - N. J. A. Sloane, Dec 05 2012
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REFERENCES
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David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, pp. 15-16.
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LINKS
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EXAMPLE
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There are six ways to dissect a square into four rectangles of equal area, so a(4)=6:
+-+-----+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+
| | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | |
| +--+--+ | | | | | +-----+ | | | | | | | | | | | |
| | | | | | +---+ | | | | | | | | | +---+ | +---+---+
| | | | | | | | | |_____| | | | | | | | | | | | |
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+-+--+--+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+
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CROSSREFS
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KEYWORD
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hard,more,nonn,nice
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AUTHOR
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Hans Riesebos (hans.riesebos(AT)wanadoo.nl) and Herman Beeksma, Jun 03 2005
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STATUS
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approved
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