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A268339
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Number of polyominoes with width and height equal to n that are invariant under all symmetries of the square.
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3
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1, 1, 3, 3, 17, 17, 163, 163, 2753, 2753, 84731, 84731, 4879497, 4879497, 535376723, 535376723, 112921823249, 112921823249, 45931435159067, 45931435159067, 36048888105745113, 36048888105745113, 54568015172025197171, 54568015172025197171, 159197415409641803530753, 159197415409641803530753
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OFFSET
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1,3
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COMMENTS
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Percolation theory focuses on patterns that provide connectivity. Polyominoes that connect all boundaries of a square are in the percolation neighborhood. This subclass of symmetric polyominoes distinguishes itself for its beauty and its unusual enumeration pattern.
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LINKS
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FORMULA
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EXAMPLE
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The ones in this example provide the connective pattern that joins all boundaries of the square.
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
1 0 1 0 1
0 1 1 1 0
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CROSSREFS
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Cf. A054247 (all unique water retention patterns for an n X n square), A268311 (polyominoes that connect all boundaries on a square), A268758.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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