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A303335 Array read by antidiagonals: T(m,n) is the number of minimum total dominating sets in the m X n king graph.

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%I A303335 #19 May 29 2025 10:40:37
%S A303335 0,1,1,2,6,2,1,9,9,1,1,4,8,4,1,4,8,1,1,8,4,3,89,3,35,3,89,3,1,56,76,9,
%T A303335 9,76,56,1,2,16,17,1,1,1,17,16,2,9,64,1,130,9,9,130,1,64,9,4,780,6,16,
%U A303335 60,8684,60,16,6,780,4,1,304,229,1,89,493,493,89,1,229,304,1
%N A303335 Array read by antidiagonals: T(m,n) is the number of minimum total dominating sets in the m X n king graph.
%C A303335 The minimum size of a total dominating set is the total domination number A303378(m, n).
%H A303335 Andrew Howroyd, <a href="/A303335/b303335.txt">Table of n, a(n) for n = 1..435</a>
%H A303335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>.
%H A303335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumTotalDominatingSet.html">Minimum Total Dominating Set</a>.
%e A303335 Table begins:
%e A303335 =========================================
%e A303335 m\n| 1  2  3   4  5    6   7   8    9
%e A303335 ---+-------------------------------------
%e A303335 1  | 0  1  2   1  1    4   3   1    2 ...
%e A303335 2  | 1  6  9   4  8   89  56  16   64 ...
%e A303335 3  | 2  9  8   1  3   76  17   1    6 ...
%e A303335 4  | 1  4  1  35  9    1 130  16    1 ...
%e A303335 5  | 1  8  3   9  1    9  60  89   45 ...
%e A303335 6  | 4 89 76   1  9 8684 493   1   50 ...
%e A303335 7  | 3 56 17 130 60  493 208  40   32 ...
%e A303335 8  | 1 16  1  16 89    1  40 604    1 ...
%e A303335 9  | 2 64  6   1 45   50  32   1 1192 ...
%e A303335 ...
%Y A303335 Rows 1..2 are A302654, A350817.
%Y A303335 Main diagonal is A303156.
%Y A303335 Cf. A303114, A303293, A303378, A332390, A350815.
%K A303335 nonn,tabl
%O A303335 1,4
%A A303335 _Andrew Howroyd_, Apr 21 2018