This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274138 #22 Oct 28 2019 02:41:05 %S A274138 1,1,1,1,1,1,1,2,2,2,1,2,2,2,3,1,2,2,3,3,3,1,2,3,3,3,4,4,1,2,3,3,4,4, %T A274138 5,5,1,2,3,4,4,4,5,5,5,1,2,3,4,4,4,5,5,5,5,1,2,3,4,4,5,5,6,5,5,5,1,2, %U A274138 3,4,4,5,5,6,6,6,6,6,1,2,3,4,5,5,6,6,6,7,7,7,7,1,2,3,4,5,6,6,6,6,7,7,8,8,8 %N A274138 Triangle read by rows: Domination number for rectangular queens' graph Q(n,m), 1 <= n <= m. %C A274138 The queens graph Q(n X m) has the squares of the n X m chessboard as its vertices; two squares are adjacent if they are both in the same row, column, or diagonal of the board. A set D of squares of Q(n X m) is a dominating set for Q(n X m) if every square of Q(n X m) is either in D or adjacent to a square in D. The minimum size of a dominating set of Q(n X m) is the domination number, denoted by gamma(Q(n X m)). %C A274138 Less formally, gamma(Q(n X m)) is the number of queens that are necessary and sufficient to all squares of the n X m chessboard be occupied or attacked. %C A274138 Chessboard 8 X 11 is of special interest, because it cannot be dominated by 5 queens, although the larger boards 9 X 11, 10 X 11 and 11 X 11 are. It is conjectured that 8 X 11 is the only counterexample of this kind of monotonicity. %H A274138 Sandor Bozoki, <a href="/A274138/b274138.txt">Table of n, a(n) for n = 1..170</a> %H A274138 S. Bozóki, P. Gál, I. Marosi, W. D. Weakley, <a href="http://arxiv.org/abs/1606.02060">Domination of the rectangular queen’s graph</a>, arXiv:1606.02060 [math.CO], 2016. %H A274138 S. Bozóki, P. Gál, I. Marosi, W. D. Weakley, <a href="http://www.sztaki.mta.hu/~bozoki/queens/">Domination of the rectangular queen’s graph</a>, 2016. %e A274138 Table begins %e A274138 m\n|1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 %e A274138 -------------------------------------------------------- %e A274138 1 |1 %e A274138 2 |1 1 %e A274138 3 |1 1 1 %e A274138 4 |1 2 2 2 %e A274138 5 |1 2 2 2 3 %e A274138 6 |1 2 2 3 3 3 %e A274138 7 |1 2 3 3 3 4 4 %e A274138 8 |1 2 3 3 4 4 5 5 %e A274138 9 |1 2 3 4 4 4 5 5 5 %e A274138 10 |1 2 3 4 4 4 5 5 5 5 %e A274138 11 |1 2 3 4 4 5 5 6 5 5 5 %e A274138 12 |1 2 3 4 4 5 5 6 6 6 6 6 %e A274138 13 |1 2 3 4 5 5 6 6 6 7 7 7 7 %e A274138 14 |1 2 3 4 5 6 6 6 6 7 7 8 8 8 %e A274138 15 |1 2 3 4 5 6 6 6 7 7 7 8 8 8 9 %e A274138 16 |1 2 3 4 5 6 6 7 7 7 8 8 8 9 9 9 %e A274138 17 |1 2 3 4 5 6 7 7 7 8 8 8 9 9 9 9 9 %e A274138 18 |1 2 3 4 5 6 7 7 8 8 8 8 9 9 9 9 9 9 %Y A274138 Diagonal elements are in A075458: Domination number for queens' graph Q(n). %K A274138 nonn,tabl %O A274138 1,8 %A A274138 _Sandor Bozoki_, Jun 11 2016