A286194 Number of (n,2)-polyominoes.

0, 2, 11, 60, 302, 1522

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.

Links

Table of n, a(n) for n=1..6.

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) 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:
1001 100
     001

Crossrefs

Cf. A286344, A286345.

Sequence in context: A228868 A290116 A251180 * A164034 A240548 A255549

Adjacent sequences: A286191 A286192 A286193 * A286195 A286196 A286197

Keyword

nonn,more

Author

Dmitry Kamenetsky, May 05 2017

Status

approved