A polyomino of order n is an arrangement of n unit squares joined along their edges. Popular polyominoes include dominoes (n=2), tetrominoes (n=4), and pentominoes (n=5).
Here is a graphic display of the 5 tetrominoes (remember Tetris?):
The program used to generate polyominoes allows the polyominoes to contain holes. Here are examples of polyominoes with a hole:
The number of n cell polyominoes (that allow holes) for n = 1,2,...,15, is 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238951, 901971, 3426576. This is sequence A000105(M1425) in Neil J. Sloane's database of integer sequences.
The number of n cell polyominoes (without holes) for n = 1,2,...,15, is 1, 1, 2, 5, 12, 35, 107, 363, 1248, 4460, 16094, 58937, 217117, 805475, 3001211. This is sequence A000104(M1424) in Neil J. Sloane's database of integer sequences.
The program used is due to John Boyer, and is based on a paper of Redelmeier (Discrete Math. 36 (1981) 191-203).