

A234008


Free polyominoes with 2n squares, having 180degree rotational symmetry about a square midside, but no reflective symmetry.


11



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
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OFFSET

1,3


COMMENTS

The number of free polyominoes of size 2n that have 180degree 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 oddsized polyominoes cannot have the required symmetry.
The sequence enumerates a subset of the polyominoes enumerated by A006747.


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CROSSREFS



KEYWORD

nonn,hard


AUTHOR



EXTENSIONS



STATUS

approved



