cp's OEIS Frontend

A118797 Number of cells in smallest polyomino with n holes.

%I A118797 #29 Oct 13 2022 04:55:50
%S A118797 7,11,14,17,19,23,25,28,30,33,35,38,40,43,45,48,50,53,55,57,59,62,64,
%T A118797 67,69,71,74,76,78,81,83,85,88,90,92,95,97,99,101,104,106,108,110,113,
%U A118797 115,117,119,122,124,126,128,131,133,135,137,140,142,144,146,149
%N A118797 Number of cells in smallest polyomino with n holes.
%C A118797 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
%C A118797 From _Dmitry Kamenetsky_, Feb 28 2017: (Start)
%C A118797 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:
%C A118797    XXXXXXXXXXX
%C A118797    X X X X X X
%C A118797    XX X X X X X
%C A118797     XXXXXXXXXXX
%C A118797 Each new hole requires an additional 3 cells (X) to surround it. Hence we get a(n) <= 3n + 5. (End)
%H A118797 Greg Malen and Érika Roldán, <a href="https://arxiv.org/abs/1910.10342">Topology and Geometry of Crystallized Polyominoes</a>, arXiv:1910.10342 [math.CO], 2019.
%H A118797 Tomás Oliveira e Silva, <a href="http://www.ieeta.pt/%7Etos/animals/a44.html">Animal enumerations on the {4,4} Euclidean tiling</a>
%e A118797 a(1) = 7 from
%e A118797   XX
%e A118797   X X
%e A118797   XXX
%Y A118797 Cf. A168339.
%K A118797 more,nonn
%O A118797 1,1
%A A118797 _Franklin T. Adams-Watters_, May 22 2006
%E A118797 a(8) added by _Dmitry Kamenetsky_, Feb 28 2017
%E A118797 a(9)-a(60) added by _Peter Kagey_, Oct 28 2019, from Table 2 of the Malen Roldán paper.