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 A299029 #18 Feb 16 2025 08:33:53 %S A299029 1,1,1,1,1,1,1,2,2,3,1,2,2,3,3,1,2,2,3,3,4,1,2,3,3,4,4,4,1,2,3,4,4,4, %T A299029 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 A299029 3,4,4,5,5,6,6,6,6,7,1,2,3,4,5,5,6,6,6,7,7,7,7,1,2,3,4,5,6,6,6,6,7,7,8,8,8 %N A299029 Triangle read by rows: Independent domination number for rectangular queens graph Q(n,m), 1 <= n <= m. %C A299029 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 an independent dominating set of Q(n X m) is the independent domination number, denoted by i(Q(n X m)). %C A299029 Less formally, i(Q(n X m)) is the number of independent queens that are necessary and sufficient to all squares of the n X m chessboard be occupied or attacked. %C A299029 Chessboards 8 X 11 and 18 X 11 are of special interest, because they cannot be dominated by 5 and 8 independent queens, respectively, although the larger boards 9 X 11, 10 X 11, 11 X 11 and 18 X 12 are. It is open how many such counterexamples of this kind of monotonicity exist. %H A299029 Sandor Bozoki, <a href="/A299029/b299029.txt">First 18 rows of the triangle, formatted as a simple linear sequence n, a(n) for n = 1..171</a> %H A299029 S. Bozóki, P. Gál, I. Marosi, W. D. Weakley, <a href="http://arxiv.org/abs/1606.02060">Domination of the rectangular queens graph</a>, arXiv:1606.02060 [math.CO], 2016. %H A299029 S. Bozóki, P. Gál, I. Marosi, W. D. Weakley, <a href="http://www.sztaki.mta.hu/~bozoki/queens/">Domination of the rectangular queens graph</a>, 2016. %H A299029 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QueenGraph.html">Queen Graph</a> %H A299029 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QueensProblem.html">Queens Problem</a> %e A299029 Table begins %e A299029 m\n| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 %e A299029 ---+----------------------------------------------------- %e A299029 1 | 1 %e A299029 2 | 1 1 %e A299029 3 | 1 1 1 %e A299029 4 | 1 2 2 3 %e A299029 5 | 1 2 2 3 3 %e A299029 6 | 1 2 2 3 3 4 %e A299029 7 | 1 2 3 3 4 4 4 %e A299029 8 | 1 2 3 4 4 4 5 5 %e A299029 9 | 1 2 3 4 4 4 5 5 5 %e A299029 10 | 1 2 3 4 4 4 5 5 5 5 %e A299029 11 | 1 2 3 4 4 5 5 6 5 5 5 %e A299029 12 | 1 2 3 4 4 5 5 6 6 6 6 7 %e A299029 13 | 1 2 3 4 5 5 6 6 6 7 7 7 7 %e A299029 14 | 1 2 3 4 5 6 6 6 6 7 7 8 8 8 %e A299029 15 | 1 2 3 4 5 6 6 7 7 7 7 8 8 9 9 %e A299029 16 | 1 2 3 4 5 6 6 7 7 7 8 8 8 9 9 9 %e A299029 17 | 1 2 3 4 5 6 7 7 7 8 8 8 9 9 9 9 9 %e A299029 18 | 1 2 3 4 5 6 7 7 8 8 9 8 9 9 9 10 10 10 %Y A299029 Diagonal elements are in A075324: Independent domination number for queens graph Q(n). %Y A299029 Cf. A274138: Domination number for rectangular queens graph Q(n,m). %Y A299029 Cf. A279404: Independent domination number for queens graph on an n X n toroidal board. %K A299029 nonn,tabl %O A299029 1,8 %A A299029 _Sandor Bozoki_, Feb 01 2018