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%I #29 Apr 07 2020 21:39:41
%S 0,2,11,60,302,1522
%N Number of (n,2)-polyominoes.
%C (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 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 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) two 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 3. Here are all such polyominoes for n=2:
%e 1001 100
%e 001
%Y Cf. A286344, A286345.
%K nonn,more
%O 1,2
%A _Dmitry Kamenetsky_, May 05 2017
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