
COMMENTS

The rectangles are distinguishable by aspect ratio, not size.
A rectangle is dissectable into squares if and only if its sides are commensurable. A rectangle with commensurable sides is dissectable into n squares for all but a finite number of positive integers n. For example, a square is dissectable into any number of squares other than 2, 3, or 5.


EXAMPLE

For n = 3 the a(3) = 2 rectangles are 3X1 and 3X2. For example, a 3X2 rectangle can be tiled by a 2X2 square and two 1X1 squares.
For n = 4 the a(4) = 5 rectangles are 1X1, 4X1, 4X3, 5X2 and 5X3.
For n = 5 the a(5) = 11 rectangles are 2X1, 5X1, 5X4, 6X5, 7X2, 7X3, 7X4, 7X5, 7X6, 8X3 and 8X5.
For n = 6 the a(6) = 28 rectangles are 1X1, 3X1, 3X2, 4X3, 5X4, 6X1, 6X5, 9X2, 9X4, 9X5, 9X7, 10X3, 10X7, 10X9, 11X3, 11X4, 11X5, 11X6, 11X7, 11X8, 11X10, 12X5, 12X7, 13X5, 13X6, 13X7, 13X8 and 13X11.
