Catalogue of Unitary Polyominoes
Introduction
A polyomino is a figure made of equal squares joined
edge to edge.
A unitary polyomino is one whose edges all have length 1.
If we color the cells of a unitary polyomino with red and black checks,
all cells on each boundary will have the same color.
In the example at the right, the cells on the outer boundary are all red,
and the cells on the boundary of the hole are all black.
See also Catalogue of Almost Unitary
Polyominoes,
Catalogue of Unitary Polyiamonds,
and
Catalogue of Unitary Polycubes.
Enumeration
Cells  1  5  8  9  11  12
 13  14  15  16  17  18  19  20 
Unitary Polyominoes A245620
 1  1  1  1  2  2  3  4  7  10  17  28  47  69


Holeless Unitary Polyominoes A245660
 1  1  1  1  2  1  2  4  5  4  12  13  20  29

In 2023, John Mason continued the enumeration of holeless
unitary polyominoes to 50 cells.
See the link above.
1 Cell
5 Cells
8 Cells
9 Cells
11 Cells
12 Cells
13 Cells
14 Cells
15 Cells
16 Cells
17 Cells
18 Cells
19 Cells
20 Cells
Last revised 20230501.
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Col. George Sicherman
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