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%I #14 Apr 22 2018 04:51:42
%S 0,1,1,2,4,2,1,1,1,1,1,16,2,16,1,4,9,1,1,9,4,3,1,3,16,3,1,3,1,64,4,
%T 256,256,4,64,1,2,16,4,4,160,4,4,16,2,9,1,9,121,25,25,121,9,1,9,4,169,
%U 12,2916,268,144,268,2916,12,169,4
%N Array read by antidiagonals: T(m,n) = number of minimum total dominating sets in the grid graph P_m X P_n.
%C The minimum size of a total dominating set is the total domination number A300358(m, n).
%H Andrew Howroyd, <a href="/A303293/b303293.txt">Table of n, a(n) for n = 1..435</a> (first 29 antidiagonals)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%e Table begins:
%e ===============================================
%e m\n| 1 2 3 4 5 6 7 8 9
%e ---+-------------------------------------------
%e 1 | 0 1 2 1 1 4 3 1 2 ...
%e 2 | 1 4 1 16 9 1 64 16 1 ...
%e 3 | 2 1 2 1 3 4 4 9 12 ...
%e 4 | 1 16 1 16 256 4 121 2916 25 ...
%e 5 | 1 9 3 256 160 25 268 4225 510 ...
%e 6 | 4 1 4 4 25 144 529 2025 10404 ...
%e 7 | 3 64 4 121 268 529 4 441 630 ...
%e 8 | 1 16 9 2916 4225 2025 441 256 9 ...
%e 9 | 2 1 12 25 510 10404 630 9 1364 ...
%e ...
%Y Rows 1..2 are A302654, A303054.
%Y Main diagonal is A303142.
%Y Cf. A300358, A303111, A303118.
%K nonn,tabl
%O 1,4
%A _Andrew Howroyd_, Apr 20 2018
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