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A332390 Array read by antidiagonals: T(m,n) is the number of minimal total dominating sets in the m X n king graph.

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%I A332390 #14 May 22 2025 22:34:02
%S A332390 0,1,1,2,6,2,1,10,10,1,2,15,20,15,2,4,52,52,52,52,4,3,105,179,141,179,
%T A332390 105,3,4,175,418,801,801,418,175,4,8,481,1167,2950,7770,2950,1167,481,
%U A332390 8,9,1028,3498,9792,34790,34790,9792,3498,1028,9,10,2000,9074,47527,184318,204372,184318,47527,9074,2000,10
%N A332390 Array read by antidiagonals: T(m,n) is the number of minimal total dominating sets in the m X n king graph.
%H A332390 Andrew Howroyd, <a href="/A332390/b332390.txt">Table of n, a(n) for n = 1..120</a>
%H A332390 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>.
%H A332390 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalTotalDominatingSet.html">Minimal Total Dominating Set</a>.
%F A332390 T(n,m) = T(m,n).
%e A332390 Array begins:
%e A332390 ================================================================
%e A332390 m\n | 1   2    3     4       5        6         7          8
%e A332390 ----+-----------------------------------------------------------
%e A332390   1 | 0   1    2     1       2        4         3          4 ...
%e A332390   2 | 1   6   10    15      52      105       175        481 ...
%e A332390   3 | 2  10   20    52     179      418      1167       3498 ...
%e A332390   4 | 1  15   52   141     801     2950      9792      47527 ...
%e A332390   5 | 2  52  179   801    7770    34790    184318    1305358 ...
%e A332390   6 | 4 105  418  2950   34790   204372   1593094   14720683 ...
%e A332390   7 | 3 175 1167  9792  184318  1593094  16260853  231301551 ...
%e A332390   8 | 4 481 3498 47527 1305358 14720683 231301551 4570906041 ...
%e A332390   ...
%Y A332390 Rows 1..4 are A302655, A332392, A332393, A332394.
%Y A332390 Main diagonal is A332391.
%Y A332390 Cf. A286849, A303114, A303118, A303335, A303378.
%K A332390 nonn,tabl
%O A332390 1,4
%A A332390 _Andrew Howroyd_, Feb 10 2020