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 A286344 #22 Feb 16 2025 10:26:42 %S A286344 0,2,4,20,68,289,1151,4792,19603,80820,331373 %N A286344 Number of (n,1)-polyominoes. %C A286344 (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. %C A286344 Number of distinct n-cell subsets of (n+1)-celled polyominoes that are not polyominoes. - _Charlie Neder_, Feb 12 2019 %H A286344 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 A286344 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) one 0 to make all the 1s connected. This also means that the Manhattan distance between any pair of 1s is at most 2. Here are all such polyominoes for n=3: %e A286344 1101 100 100 010 %e A286344 101 011 101 %Y A286344 Cf. A286194, A286345, A381030. %K A286344 nonn,more %O A286344 1,2 %A A286344 _Dmitry Kamenetsky_, May 07 2017 %E A286344 a(6)-a(7) corrected and a(8)-a(11) added by _John Mason_, Feb 15 2025