A118797 Number of cells in smallest polyomino with n holes.

7, 11, 14, 17, 19, 23, 25, 28, 30, 33, 35, 38, 40, 43, 45, 48, 50, 53, 55, 57, 59, 62, 64, 67, 69, 71, 74, 76, 78, 81, 83, 85, 88, 90, 92, 95, 97, 99, 101, 104, 106, 108, 110, 113, 115, 117, 119, 122, 124, 126, 128, 131, 133, 135, 137, 140, 142, 144, 146, 149

Offset: 1

Author

Franklin T. Adams-Watters, May 22 2006

Keywords

• more
• nonn

Comments

The polyomino must be rook-wise connected and a hole is a collection of rook-wise connected empty cells from which a rook cannot escape. - N. J. A. Sloane, May 25 2006

From Dmitry Kamenetsky, Feb 28 2017: (Start)

There is a simple pattern that gives us a good upper bound. The idea is to use two rows of single-cell holes touching at their corners:

XXXXXXXXXXX

X X X X X X

XX X X X X X

XXXXXXXXXXX

Each new hole requires an additional 3 cells (X) to surround it. Hence we get a(n) <= 3n + 5. (End)

Examples

			a(1) = 7 from
  XX
  X X
  XXX
		

Links

• Greg Malen and Érika Roldán, Topology and Geometry of Crystallized Polyominoes, arXiv:1910.10342 [math.CO], 2019.
• Tomás Oliveira e Silva, Animal enumerations on the {4,4} Euclidean tiling

Crossrefs

Cf. A168339.

Extensions

a(8) added by Dmitry Kamenetsky, Feb 28 2017

a(9)-a(60) added by Peter Kagey, Oct 28 2019, from Table 2 of the Malen Roldán paper.