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Array read by antidiagonals: T(m,n) = number of total dominating sets in the grid graph P_m X P_n.
6

%I #8 Apr 18 2018 19:56:35

%S 0,1,1,3,9,3,4,25,25,4,5,81,161,81,5,9,289,961,961,289,9,16,961,6235,

%T 11236,6235,961,16,25,3249,39601,137641,137641,39601,3249,25,39,11025,

%U 251433,1677025,3270375,1677025,251433,11025,39

%N Array read by antidiagonals: T(m,n) = number of total dominating sets in the grid graph P_m X P_n.

%C Equivalently, the number of n X m binary matrices with every element adjacent to some 0 horizontally or vertically.

%H Andrew Howroyd, <a href="/A303111/b303111.txt">Table of n, a(n) for n = 1..435</a>

%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

%e ---|-------------------------------------------------------------------

%e 1 | 0 1 3 4 5 9 16 ...

%e 2 | 1 9 25 81 289 961 3249 ...

%e 3 | 3 25 161 961 6235 39601 251433 ...

%e 4 | 4 81 961 11236 137641 1677025 20430400 ...

%e 5 | 5 289 6235 137641 3270375 76405081 1783064069 ...

%e 6 | 9 961 39601 1677025 76405081 3416753209 152598828321 ...

%e 7 | 16 3249 251433 20430400 1783064069 152598828321 13057656650476 ...

%e ...

%Y Rows 1..2 are A195971(n-1), A141583(n+1).

%Y Main diagonal is A133793.

%Y Cf. A218354 (dominating sets), A291872 (connected dominating sets).

%Y Cf. A303114 (king graph), A303118 (minimal total dominating sets).

%K nonn,tabl

%O 1,4

%A _Andrew Howroyd_, Apr 18 2018