A234008 Free polyominoes with 2n squares, having 180-degree rotational symmetry about a square mid-side, but no reflective symmetry.

0, 1, 4, 16, 60, 231, 877, 3362, 12905, 49825, 193003, 750581, 2927792, 11453171, 44911853, 176499605, 694954416, 2741031257, 10827727980, 42831355495, 169640762209, 672657218163, 2669990735153, 10608176066076, 42184579054003

Offset: 1

Author

John Mason, Dec 18 2013

Keywords

• nonn
• hard

Comments

The number of free polyominoes of size 2n that have 180-degree rotational symmetry about a point that coincides with the midpoint of a side a square, and that have not at the same time any reflective symmetry. Note that for polyominoes which have a hole in the center, the center of rotation will be the midpoint of a side of a square within the hole, rather than being the midpoint of a side of a square of the polyomino itself. The sequence is defined for 2n rather than n as odd-sized polyominoes cannot have the required symmetry.

The sequence enumerates a subset of the polyominoes enumerated by A006747.

Crossrefs

Cf. A000105, A001933, A234006, A234007, A234009, A234010, A006747.

Extensions

a(12)-a(18) from John Mason, Dec 13 2021

a(19)-a(25) from John Mason, Apr 15 2023