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A350820 Array read by antidiagonals: T(m,n) is the number of minimum dominating sets in the grid graph P_m X P_n.

%I A350820 #16 Feb 16 2025 08:34:02
%S A350820 1,2,2,1,6,1,4,3,3,4,3,12,10,12,3,1,2,29,29,2,1,8,17,1,2,1,17,8,4,2,2,
%T A350820 52,52,2,2,4,1,20,11,92,22,92,11,20,1,13,2,46,2,13,13,2,46,2,13,5,24,
%U A350820 1,4,3,288,3,4,1,24,5,1,2,3,324,344,34,34,344,324,3,2,1
%N A350820 Array read by antidiagonals: T(m,n) is the number of minimum dominating sets in the grid graph P_m X P_n.
%C A350820 The domination number of the grid graphs is tabulated in A350823.
%H A350820 Stephan Mertens, <a href="/A350820/b350820.txt">Table of n, a(n) for n = 1..946</a> (first 276 terms from Andrew Howroyd)
%H A350820 Stephan Mertens, <a href="https://arxiv.org/abs/2408.08053">Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph</a>, arXiv:2408.08053 [math.CO], Aug 2024.
%H A350820 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H A350820 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>
%F A350820 T(m,n) = T(n,m).
%e A350820 Table begins:
%e A350820 ===================================
%e A350820 m\n | 1  2  3  4   5   6  7   8
%e A350820 ----+------------------------------
%e A350820   1 | 1  2  1  4   3   1  8   4 ...
%e A350820   2 | 2  6  3 12   2  17  2  20 ...
%e A350820   3 | 1  3 10 29   1   2 11  46 ...
%e A350820   4 | 4 12 29  2  52  92  2   4 ...
%e A350820   5 | 3  2  1 52  22  13  3 344 ...
%e A350820   6 | 1 17  2 92  13 288 34   2 ...
%e A350820   7 | 8  2 11  2   3  34  2  34 ...
%e A350820   8 | 4 20 46  4 344   2 34  52 ...
%e A350820   ...
%Y A350820 Rows 1..4 are A347633, A347558, A350821, A350822.
%Y A350820 Main diagonal is A347632.
%Y A350820 Cf. A218354 (dominating sets), A286847 (minimal dominating sets), A303293, A350815, A350823.
%K A350820 nonn,look,tabl
%O A350820 1,2
%A A350820 _Andrew Howroyd_, Jan 17 2022