A pseudo-polyomino, also called a polyking, polyplet or hinged polyomino, is a plane geometric figure formed by joining one or more equal squares edge-to-edge or corner-to-corner at 90°. It is a polyform with square cells. The polyominoes are a subset of the polykings.
The name "polyking" refers to the king in chess. The n-kings are the n-square shapes which could be occupied by a king on an infinite chessboard in the course of legal moves.
Golomb uses the term pseudo-polyomino referring to kingwise-connected sets of squares.
There are three common ways of distinguishing polyominoes and polykings for enumeration:
The following table shows the numbers of polykings of various types with n cells.
| n | free | one-sided | fixed | |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | |
| 2 | 2 | 2 | 4 | |
| 3 | 5 | 6 | 20 | |
| 4 | 22 | 34 | 110 | |
| 5 | 94 | 166 | 638 | |
| 6 | 524 | 991 | 3832 | |
| 7 | 3,031 | 5,931 | 23,592 | |
| 8 | 18,770 | 37,196 | 147,941 | |
| 9 | 118,133 | 235,456 | 940,982 | |
| 10 | 758,381 | 1,514,618 | 6,053,180 | |
| 11 | 4,915,652 | 9,826,177 | 39,299,408 | |
| 12 | 32,149,296 | 64,284,947 | 257,105,146 | |