Two-sided polyenns may be rotated and reflected. One-sided polyenns may be rotated but not reflected. Thus two distinct mirror images of a polyenn are regarded as distinct one-sided polyenns.
| Cells | Two-Sided | One-Sided |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 1 |
| 3 | 3 | 3 |
| 4 | 14 | 24 |
| 5 | 82 | 148 |
| 6 | 585 | 1 145 |
| 7 | 4 418 | 8 728 |
| 8 | 34 838 | 69 503 |
Matthias Koch and
Sascha Kurz have enumerated polyenns up through 13 cells.
See Matthias Koch and Sascha Kurz, Enumeration of Generalized
Polyominoes.
The enumeration for two-sided polyenns is A103467 in the On-Line Encyclopedia of Integer Sequences.
The figures below show two-sided polyenns.
Last revised 2024-03-27.