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A108066 Number of distinct ways to dissect a square into n rectangles of equal area. 5
1, 1, 2, 6, 18, 65, 281, 1343, 6953, 38023 (list; graph; refs; listen; history; text; internal format)
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

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

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

LINKS

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

R. Haggkvist, P.-O. Lindberg, and B. Bindstrom, 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:

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

| |     | | | |   | | |     | | | | | | | |   | | |   |   |

| |     | | | |   | | |     | | | | | | | |   | | |   |   |

| +--+--+ | | |   | | +-----+ | | | | | | |   | | |   |   |

| |  |  | | | +---+ | |     | | | | | | | +---+ | +---+---+

| |  |  | | | |   | | |_____| | | | | | | |   | | |   |   |

| |  |  | | | |   | | |     | | | | | | | |   | | |   |   |

| |  |  | | | |   | | |     | | | | | | | |   | | |   |   |

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

CROSSREFS

Cf. A189243, A219861.

Sequence in context: A150073 A150074 A300335 * A052863 A037128 A150075

Adjacent sequences:  A108063 A108064 A108065 * A108067 A108068 A108069

KEYWORD

hard,more,nonn,nice

AUTHOR

Hans Riesebos (hans.riesebos(AT)wanadoo.nl) and Herman Beeksma, Jun 03 2005

STATUS

approved

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Last modified June 20 17:51 EDT 2019. Contains 324234 sequences. (Running on oeis4.)