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A286344 Number of (n,1)-polyominoes. 2
0, 2, 4, 20, 68, 288, 1138 (list; graph; refs; listen; history; text; internal format)



(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.

Number of distinct n-cell subsets of (n+1)-celled polyominoes that are not polyominoes. - Charlie Neder, Feb 12 2019


Table of n, a(n) for n=1..7.

Dmitry Kamenetsky and Tristrom Cooke, Tiling rectangles with holey polyominoes, arXiv:1411.2699 [cs.CG], 2015.


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:

1101 100 100 010

     101 011 101


Cf. A286194, A286345.

Sequence in context: A274520 A238229 A192377 * A279153 A204550 A009291

Adjacent sequences:  A286341 A286342 A286343 * A286345 A286346 A286347




Dmitry Kamenetsky, May 07 2017



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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)