A108066 - OEIS

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A108066

Number of distinct ways to dissect a square into n rectangles of equal area.

1, 1, 2, 6, 18, 65, 281, 1343, 6953, 38023

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OFFSET

1,3

COMMENTS

"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

REFERENCES

David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, pp. 15-16.

LINKS

Table of n, a(n) for n=1..10.

Blanche Descartes, Divisions of a square into rectangles, Eureka, No. 34 (1971), 31-35.

R. Häggkvist, P.-O. Lindberg, and B. Lindström, Dissecting a square into rectangles of equal area, Discr. Math. 47 (1983), 321-323.

Johan Nilsson, Illustrations for terms up to a(6)..

N. J. A. Sloane, Blanche Descartes's dissection into 7 pieces with equal areas but different shapes.

Eric Weisstein, Blanche's Dissection.

EXAMPLE

There are six ways to dissect a square into four rectangles of equal area, so a(4)=6:

+-+-----+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+