A234007 Free polyominoes with 4n squares, having 90-degree rotational symmetry about a square corner, but not having reflective symmetry.

0, 1, 2, 9, 30, 110, 387, 1419, 5185, 19225, 71634, 269250, 1017260, 3864267, 14742260, 56470053, 217052829, 836878982

Offset: 1

Author

John Mason, Dec 18 2013

Keywords

• nonn
• more

Comments

The number of free polyominoes of size 4n that have 90-degree rotational symmetry about a point that coincides with the corner of a square, and that have not at the same time reflective symmetry. Note that for polyominoes which have a hole in the center, the center of rotation will be the corner of a square within the hole, rather than being the corner of a square of the polyomino itself. The sequence is defined for 4n rather than n as polyominoes of size not a multiple of 4 cannot have the required symmetry.

The sequence enumerates a subset of the polyominoes enumerated by A144553.

Crossrefs

Cf. A000105, A001933, A234006, A234008, A234009, A234010, A144553.

Extensions

a(8)-a(13) from Sean A. Irvine, Jul 04 2019

a(14)-a(18) from John Mason, Feb 02 2022