Corrections to table in Dr. Math article, http://mathforum.org/library/drmath/view/57699.html.
Ray Chandler, rayjchandler(AT)sbcglobal.net, May 10, 2011.

Corrections are denoted by *.  I split the 1x1 column into two parts to better show the pattern.  
Column 1x1a counts the rhombi of types 2 and 3 described below; 1x1b counts those of type 1, 
which fits the pattern of the following columns.  


Size of rhombus in cm

                     1x1a  1x1b  2x2    3x3   4x4   5x5      Total
     1 by 1 cm        1     1     0      0     0     0          1
     2 by 2           4     4     1      0     0     0          9
     3 by 3          12     9     4      1     0     0         26
     4 by 4          24    16     9*     4     1     0         54*
     5 by 5          40    25    16*     9     4     1         95*
      
        ____________                                                                       
       /\    /\    /                                                   
      /  \  /  \  /                                                    
     /____\/____\/                                                     
    /\    /\    /                                                      
   /  \  /  \  /                                                       
  /____\/____\/                                                        
                                                                       
Here is a rough diagram of the rhombus type we are investigating. This 
is a 2x2 rhombus and as you can see it is divided into equilateral     
triangles as opposed to just smaller 1x1 rhombi. If you draw it out on 
paper more accurately with the diagonals going directly into the       
corner you will easily see 9 rhombi.                                   
                                                                       
We have investigated this type of rhombus and we know there are three  
types of rhombi to be found within these rhombi. They are roughly      
drawn below.                                                           
                                                                       
      _               __                                               
     /_/      /\      \_\                                              
              \/                                                       
                                                                       
The first rhombus would have a diagonal running from top left to       
bottom right, the second has a horizontal line splitting it into 2     
equilateral triangles, and the third has a diagonal line running from  
top right to bottom left.