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A291873 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the m X n king graph.

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%I A291873 #7 Feb 16 2025 08:33:51
%S A291873 1,3,3,4,15,4,4,48,48,4,4,144,336,144,4,4,432,2192,2192,432,4,4,1296,
%T A291873 14544,29648,14544,1296,4,4,3888,96528,405648,405648,96528,3888,4,4,
%U A291873 11664,640336,5568336,11293568,5568336,640336,11664,4
%N A291873 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the m X n king graph.
%H A291873 Andrew Howroyd, <a href="/A291873/b291873.txt">Table of n, a(n) for n = 1..435</a>
%H A291873 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H A291873 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%e A291873 Array begins:
%e A291873 ======================================================================
%e A291873 m\n| 1    2      3        4          5             6               7
%e A291873 ---|------------------------------------------------------------------
%e A291873 1  | 1    3      4        4          4             4               4...
%e A291873 2  | 3   15     48      144        432          1296            3888...
%e A291873 3  | 4   48    336     2192      14544         96528          640336...
%e A291873 4  | 4  144   2192    29648     405648       5568336        76414224...
%e A291873 5  | 4  432  14544   405648   11293568     315156544      8793207424...
%e A291873 6  | 4 1296  96528  5568336  315156544   17784998912   1001953789632...
%e A291873 7  | 4 3888 640336 76414224 8793207424 1001953789632 113637188081536...
%e A291873 ...
%Y A291873 Row 2 is A188825(n) for n > 2.
%Y A291873 Main diagonal is A289180.
%Y A291873 Cf. A218663, A291872.
%K A291873 nonn,tabl
%O A291873 1,2
%A A291873 _Andrew Howroyd_, Sep 04 2017