A286344 Number of (n,1)-polyominoes.

0, 2, 4, 20, 68, 288, 1138

Offset

1,2

Comments

(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

Links

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.

Example

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

Crossrefs

Cf. A286194, A286345.

Sequence in context: A337616 A238229 A192377 * A279153 A204550 A009291

Adjacent sequences: A286341 A286342 A286343 * A286345 A286346 A286347

Keyword

nonn,more

Author

Dmitry Kamenetsky, May 07 2017

Status

approved