

A118797


Number of cells in smallest polyomino with n holes.


1



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
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OFFSET

1,1


COMMENTS

The polyomino must be rookwise connected and a hole is a collection of rookwise connected empty cells from which a rook cannot escape.  N. J. A. Sloane, May 25 2006
There is a simple pattern that gives us a good upper bound. The idea is to use two rows of singlecell 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.  Dmitry Kamenetsky, Feb 28 2017


LINKS

Table of n, a(n) for n=1..60.
Greg Malen, 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


EXAMPLE

a(1) = 7 from
XX
X X
XXX


CROSSREFS

Cf. A168339.
Sequence in context: A004236 A153049 A065105 * A080837 A168135 A225858
Adjacent sequences: A118794 A118795 A118796 * A118798 A118799 A118800


KEYWORD

more,nonn


AUTHOR

Franklin T. AdamsWatters, May 22 2006


EXTENSIONS

a(8) added by Dmitry Kamenetsky, Feb 28 2017
a(9)1(60) added by Peter Kagey, Oct 28 2019, from Table 2 of the Malen Roldán paper.


STATUS

approved



