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
