

A108066


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


5




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), 3135.
David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, pp. 1516.


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), 321323.
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



