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A268339
Number of polyominoes with width and height equal to n that are invariant under all symmetries of the square.
3
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
OFFSET
1,3
COMMENTS
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.
FORMULA
a(2*n) = a(2*n-1) = A268758(n). - Andrew Howroyd, May 03 2020
EXAMPLE
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
CROSSREFS
Cf. A054247 (all unique water retention patterns for an n X n square), A268311 (polyominoes that connect all boundaries on a square), A268758.
Sequence in context: A226610 A332840 A279172 * A224750 A014783 A090524
KEYWORD
nonn
AUTHOR
Craig Knecht, Feb 02 2016
EXTENSIONS
Terms a(17) and beyond from Andrew Howroyd, May 03 2020
STATUS
approved