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A303378 Array read by antidiagonals: T(m,n) = total domination number of the m X n king graph.

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%I A303378 #8 Feb 16 2025 08:33:54
%S A303378 1,2,2,2,2,2,2,2,2,2,3,2,2,2,3,4,3,2,2,3,4,4,4,3,4,3,4,4,4,4,4,4,4,4,
%T A303378 4,4,5,4,4,4,5,4,4,4,5,6,5,4,6,6,6,6,4,5,6,6,6,5,6,7,8,7,6,5,6,6,6,6,
%U A303378 6,6,8,8,8,8,6,6,6,6,7,6,6,8,9,8,9,8,9,8,6,6,7
%N A303378 Array read by antidiagonals: T(m,n) = total domination number of the m X n king graph.
%H A303378 Andrew Howroyd, <a href="/A303378/b303378.txt">Table of n, a(n) for n = 1..496</a>
%H A303378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H A303378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%e A303378 Table begins:
%e A303378 =======================================================
%e A303378 m\n| 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
%e A303378 ---+---------------------------------------------------
%e A303378 1  | 1  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
%e A303378 2  | 2  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
%e A303378 3  | 2  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
%e A303378 4  | 2  2  2  4  4  4  6  6  6  8  8  8 10 10 10 12 ...
%e A303378 5  | 3  3  3  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
%e A303378 6  | 4  4  4  4  6  8  8  8 10 12 12 12 14 16 16 16 ...
%e A303378 7  | 4  4  4  6  7  8  9 10 11 12 14 14 16 17 18 19 ...
%e A303378 8  | 4  4  4  6  8  8 10 12 12 14 16 16 18 20 20 22 ...
%e A303378 9  | 5  5  5  6  9 10 11 12 15 16 17 18 21 22 23 24 ...
%e A303378 ...
%Y A303378 Main diagonal is A302401.
%Y A303378 Cf. A300358, A303114, A303335.
%K A303378 nonn,tabl
%O A303378 1,2
%A A303378 _Andrew Howroyd_, Apr 22 2018