Polyare

A polyare is a polyform obtained from a polyomino by cutting each square cell into two congruent rectangles parallel to a pair of its sides and retaining one half, so that the remaining halves are connected along line segments of positive length. Some joins between cells of the original polyomino may be lost. An -are is obtained from a polyomino with cells.

The first few -ares are illustrated above. In counting free -ares, translations, rotations, and reflections are identified. For one-sided -ares, only translations and rotations are identified. The following table gives the numbers of free and one-sided -ares for , 2, ..., 8.

	-ares	one-sided -ares
Sloane	A057724	A057725
1	1	1
2	3	4
3	9	16
4	42	77
5	180	351
6	889	1747
7	4392	8745
8	22432	44724