Polyplet
A polyomino-like object made by attaching squares joined either at sides or corners. Because neighboring squares can be in relation to one
another as kings may move on a chessboard,
polyplets are sometimes also called polykings. The number of 
-polyplets (with
holes allowed) are 1, 2, 5, 22, 94, 524, 3031, ... (OEIS A030222).
The number of 
-polyplets having bilateral symmetry are
1, 2, 4, 10, 22, 57, 131, ... (OEIS A030234).
The number of 
-polyplets not having bilateral symmetry
are 0, 0, 1, 12, 72, 467, 2900, ... (OEIS A030235).
The number of fixed 
-polyplets are 1, 4, 20, 110, 638, 3832,
... (OEIS A006770). The number of one-sided
-polyplets are 1, 2, 6, 34, 166, 991, ... (OEIS
A030233).
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