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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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. - 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. Adams-Watters, 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

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Last modified September 23 12:53 EDT 2020. Contains 337310 sequences. (Running on oeis4.)