A234010 Free polyominoes with 2n squares, having 180-degree rotational symmetry about a square mid-side.

1, 2, 6, 19, 67, 241, 901, 3398, 12991, 49958, 193317, 751080, 2928956, 11455059, 44916219, 176506797, 694970938, 2741058805, 10827790934, 42831461499, 169641003412, 672657627655, 2669991663529, 10608177653227, 42184582641002

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, independently of 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.

Crossrefs

Cf. A000105, A001933, A234006, A234007, A234008, A234009, A346799.

Formula

a(n) = A346799(n) + A234008(n).

Extensions

More terms from John Mason, Dec 17 2021

More terms from John Mason, Apr 15 2023