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 A234010 Free polyominoes with 2n squares, having 180-degree rotational symmetry about a square mid-side. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS Table of n, a(n) for n=1..25. FORMULA a(n) = A346799(n) + A234008(n). CROSSREFS Cf. A000105, A001933, A234006, A234007, A234008, A234009, A346799. Sequence in context: A150093 A150094 A305118 * A360212 A121655 A250918 Adjacent sequences: A234007 A234008 A234009 * A234011 A234012 A234013 KEYWORD nonn,hard AUTHOR John Mason, Dec 18 2013 EXTENSIONS More terms from John Mason, Dec 17 2021 More terms from John Mason, Apr 15 2023 STATUS approved

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Last modified August 6 06:32 EDT 2024. Contains 374960 sequences. (Running on oeis4.)