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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..16.

Craig Knecht, Change of state - math becomes art

Craig Knecht, Polyominoe enumeration

Wikipedia, Connective polyominoes with 4 sym-axis

Wikipedia, Water Retention on Mathematical Surfaces

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).

Sequence in context: A231908 A226610 A279172 * A224750 A014783 A090524

Adjacent sequences:  A268336 A268337 A268338 * A268340 A268341 A268342

KEYWORD

nonn

AUTHOR

Craig Knecht, Feb 02 2016

STATUS

approved

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Last modified November 16 03:09 EST 2018. Contains 317252 sequences. (Running on oeis4.)