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A324407
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Number of unoriented polyomino rings of length 4n with fourfold rotational symmetry.
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10
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1, 1, 1, 2, 3, 6, 10, 21, 38, 80, 157, 336, 691, 1493, 3164, 6900, 14880, 32647, 71212, 157069, 345216, 764666, 1689978, 3756879, 8338405, 18593389, 41410352, 92583361, 206790477, 463400376, 1037575558, 2329839141, 5227759707, 11759828568, 26436550400
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OFFSET
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1,4
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COMMENTS
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Redelmeier uses these rings to enumerate polyominoes of the regular tiling {4,4} with fourfold rotational symmetry (A144553) and an even number of cells. Each cell of a polyomino ring is adjacent to (shares an edge with) exactly two other cells. For unoriented rings, a chiral ring and its congruent reflection are counted as one.
For n odd, the center of the ring is a vertex of the tiling; for n even, the center is the center of a tile.
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LINKS
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FORMULA
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EXAMPLE
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For a(1)=1, the four cells form a square. For a(2)=1, the eight cells form a 3 X 3 square with the center cell omitted. For a(3)=1, the twelve cells form a 4 X 4 square with the four inner cells omitted. For a(4)=2, the sixteen cells of one ring form a 5 X 5 square with the nine inner cells omitted; the other ring is similar, but with each corner cell omitted and replaced with the cell diagonally toward the center from that corner cell.
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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STATUS
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approved
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