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%I #26 Apr 15 2023 05:08:33
%S 0,1,4,16,60,231,877,3362,12905,49825,193003,750581,2927792,11453171,
%T 44911853,176499605,694954416,2741031257,10827727980,42831355495,
%U 169640762209,672657218163,2669990735153,10608176066076,42184579054003
%N Free polyominoes with 2n squares, having 180-degree rotational symmetry about a square mid-side, but no reflective symmetry.
%C 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.
%C The sequence enumerates a subset of the polyominoes enumerated by A006747.
%Y Cf. A000105, A001933, A234006, A234007, A234009, A234010, A006747.
%K nonn,hard
%O 1,3
%A _John Mason_, Dec 18 2013
%E a(12)-a(18) from _John Mason_, Dec 13 2021
%E a(19)-a(25) from _John Mason_, Apr 15 2023
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