A286345 Number of (n,3)-polyominoes.

0, 3, 17, 151, 955

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..5.

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) three 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 4. Here are all such polyominoes for n=2:
10001 1000 100
      0001 000
           001

Crossrefs

Cf. A286194, A286344.

Sequence in context: A305471 A368597 A135750 * A303063 A209305 A182957

Adjacent sequences: A286342 A286343 A286344 * A286346 A286347 A286348

Keyword

nonn,more

Author

Dmitry Kamenetsky, May 07 2017

Status

approved