%I #9 Mar 26 2023 16:03:49

%S 1,1,1,1,4,1,1,12,12,1,1,32,79,32,1,1,80,408,408,80,1,1,192,1847,3600,

%T 1847,192,1,1,448,7698,26040,26040,7698,448,1,1,1024,30319,166368,

%U 281571,166368,30319,1024,1,1,2304,114606,976640,2580754,2580754,976640,114606,2304,1

%N Array read by antidiagonals: T(m,n) is the number of maximum independent sets in the 2m X 2n king graph.

%C Number of ways to tile a (2m+1) X (2n+1) board with m*n 2 X 2 tiles and 2m+2n+1 1 X 1 tiles.

%C For m,n > 0, T(m,n) is the number of minimum dominating sets in the (3m-1) X (3n-1) king graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximumIndependentVertexSet.html">Maximum Independent Vertex Set</a>

%F T(m,n) = T(n,m).

%F T(m,n) = A350818(2*m, 2*n) = A350815(3*m-1, 3*n-1).

%e Table begins:

%e =============================================

%e m\n | 0 1 2 3 4 5

%e ----+----------------------------------------

%e 0 | 1 1 1 1 1 1 ...

%e 1 | 1 4 12 32 80 192 ...

%e 2 | 1 12 79 408 1847 7698 ...

%e 3 | 1 32 408 3600 26040 166368 ...

%e 4 | 1 80 1847 26040 281571 2580754 ...

%e 5 | 1 192 7698 166368 2580754 32572756 ...

%e ...

%Y Rows 0..12 are A000012, A001787(n+1), A061593, A061594, A173782, A173783, A174154, A174155, A174558, A195648, A195649, A195650, A195651.

%Y Main diagonal is A018807.

%Y Cf. A350815, A350818.

%K nonn,tabl

%O 0,5

%A _Andrew Howroyd_, Jan 17 2022