This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268339 #24 May 03 2020 22:19:39 %S A268339 1,1,3,3,17,17,163,163,2753,2753,84731,84731,4879497,4879497, %T A268339 535376723,535376723,112921823249,112921823249,45931435159067, %U A268339 45931435159067,36048888105745113,36048888105745113,54568015172025197171,54568015172025197171,159197415409641803530753,159197415409641803530753 %N A268339 Number of polyominoes with width and height equal to n that are invariant under all symmetries of the square. %C A268339 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 A268339 Craig Knecht, <a href="/A268339/a268339.png">Change of state - math becomes art</a> %H A268339 Craig Knecht, <a href="/A268311/a268311.pdf">Polyominoe enumeration</a> %H A268339 Wikipedia, <a href="https://en.wikipedia.org/wiki/File:Connective_polyominoes_with_4_sym-axis.jpg">Connective polyominoes with 4 sym-axis</a> %H A268339 Wikipedia, <a href="http://en.wikipedia.org/wiki/Water retention on mathematical surfaces">Water Retention on Mathematical Surfaces</a> %F A268339 a(2*n) = a(2*n-1) = A268758(n). - _Andrew Howroyd_, May 03 2020 %e A268339 The ones in this example provide the connective pattern that joins all boundaries of the square. %e A268339 0 1 1 1 0 %e A268339 1 0 1 0 1 %e A268339 1 1 1 1 1 %e A268339 1 0 1 0 1 %e A268339 0 1 1 1 0 %Y A268339 Cf. A054247 (all unique water retention patterns for an n X n square), A268311 (polyominoes that connect all boundaries on a square), A268758. %K A268339 nonn %O A268339 1,3 %A A268339 _Craig Knecht_, Feb 02 2016 %E A268339 Terms a(17) and beyond from _Andrew Howroyd_, May 03 2020