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%I #16 Sep 23 2019 05:34:07
%S 1,2,10,42,358,4468,88056,2745186,134355866,10264692132,1234801357470,
%T 232966546265096,68939282741912248
%N Number of n X n 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.
%C Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's.
%C Also, the number of maximal independent vertex sets in the grid graph P_n X P_n. - _Andrew Howroyd_, May 16 2017
%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/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%e Some solutions for n=4
%e ..0..2..0..2....2..0..1..1....2..0..3..0....0..3..0..2....1..0..3..0
%e ..1..1..2..0....0..3..1..0....0..4..0..2....3..0..3..0....1..2..0..3
%e ..2..0..2..1....3..0..2..1....3..0..2..1....0..2..1..1....0..1..3..0
%e ..0..3..0..1....0..3..0..1....0..2..1..0....1..1..0..1....1..1..0..2
%t A197054 = Cases[Import["https://oeis.org/A197054/b197054.txt", "Table"], {_, _}][[All, 2]];
%t a[n_] := A197054[[2 n^2 - 2 n + 1]];
%t Table[a[n], {n, 1, 13}] (* _Jean-François Alcover_, Sep 23 2019 *)
%Y Diagonal of A197054.
%Y Cf. A006506 (independent vertex sets), A133515 (dominating sets).
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 09 2011
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