Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #24 May 03 2020 22:19:39
%S 1,1,3,3,17,17,163,163,2753,2753,84731,84731,4879497,4879497,
%T 535376723,535376723,112921823249,112921823249,45931435159067,
%U 45931435159067,36048888105745113,36048888105745113,54568015172025197171,54568015172025197171,159197415409641803530753,159197415409641803530753
%N Number of polyominoes with width and height equal to n that are invariant under all symmetries of the square.
%C 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.
%H Craig Knecht, <a href="/A268339/a268339.png">Change of state - math becomes art</a>
%H Craig Knecht, <a href="/A268311/a268311.pdf">Polyominoe enumeration</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/File:Connective_polyominoes_with_4_sym-axis.jpg">Connective polyominoes with 4 sym-axis</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Water retention on mathematical surfaces">Water Retention on Mathematical Surfaces</a>
%F a(2*n) = a(2*n-1) = A268758(n). - _Andrew Howroyd_, May 03 2020
%e The ones in this example provide the connective pattern that joins all boundaries of the square.
%e 0 1 1 1 0
%e 1 0 1 0 1
%e 1 1 1 1 1
%e 1 0 1 0 1
%e 0 1 1 1 0
%Y Cf. A054247 (all unique water retention patterns for an n X n square), A268311 (polyominoes that connect all boundaries on a square), A268758.
%K nonn
%O 1,3
%A _Craig Knecht_, Feb 02 2016
%E Terms a(17) and beyond from _Andrew Howroyd_, May 03 2020