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 A286345 #26 Feb 16 2025 10:26:39 %S A286345 0,3,17,151,955,5942,33819,184938,969972 %N A286345 Number of (n,3)-polyominoes. %C A286345 (n,k)-polyominoes are disconnected polyominoes with n visible squares and k transparent squares. Importantly, k must be the least number of transparent squares that need to be converted to visible squares to make all the visible squares connected. Note that a regular polyomino of order n is a (n,0)-polyomino, since all its visible squares are already connected. For more details see the paper by Kamenetsky and Cooke. %H A286345 Dmitry Kamenetsky and Tristrom Cooke, <a href="https://arxiv.org/abs/1411.2699">Tiling rectangles with holey polyominoes</a>, arXiv:1411.2699 [cs.CG], 2015. %e A286345 We can represent these polyominoes as binary matrices, where 1 means visible square and 0 means transparent square. Note that we need to flip (change to 1) three 0's to make all the 1's connected. This also means that the Manhattan distance between any pair of 1's is at most 4. Here are all such polyominoes for n=2: %e A286345 10001 1000 100 %e A286345 0001 000 %e A286345 001 %Y A286345 Cf. A286194, A286344, A381030. %K A286345 nonn,more %O A286345 1,2 %A A286345 _Dmitry Kamenetsky_, May 07 2017 %E A286345 a(6)-a(9) from _John Mason_, Feb 15 2025