There are 4 ways (up to symmetry) to form a nonsquare rectangle from 3 rectangles with the same area:
+-----+ +-+-+-+ +-----+ +-+---+
| | | | | | | | | | |
+-----+ | | | | +--+--+ | | |
| | | | | | | | | | +---+
+-----+ | | | | | | | | | |
| | | | | | | | | | | |
+-----+ +-+-+-+ +--+--+ +-+---+
So a(3)=4.
The eleven solutions for n=4 can be seen as a subset of the illustration of A189243(4) = 21 in that entry. - N. J. A. Sloane, Dec 05 2012
|