a(1) = 0 as no distinct oblongs can tile a square with dimensions 1 x 1.
a(2) = 0 as no distinct oblongs can tile a square with dimensions 2 x 2.
a(3) = 4. There is one tiling, excluding those equivalent by symmetry:
.
++++
 
++++
 
+ +
 
++++
.
This tiling can occur in 4 different ways, giving 4 ways in total.
a(4) = 36. The possible tilings, excluding those equivalent by symmetry, are:
.
+++++ +++++ +++++ +++++
          
+ + + +++++ + ++++ + ++++
           
+++++ + + + + + + + + +
          
+ + + + +++++ +++ +
        
+++++ +++++ +++++ +++++
.
The first tiling can occur in 8 different ways, the second in 4 different ways, the third in 16 different ways and the fourth in 8 different ways. This gives 36 ways in total.
