%I #18 Aug 24 2023 09:43:37
%S 0,1,4,8,13,20,28,38,50,61,75,90,108,124,139
%N Maximal number of unmarked cells with at least 3 marked neighboring cells in the n X n kings' graph.
%C The value of r = lim sup a(n) / n^2 is in the half-open interval [2/3, 8/11).
%C It appears from the computed terms that r = 2/3.
%H Tomas Rigaux, <a href="/A362016/a362016.py.txt">Python program</a>
%e a(2) = 1, as the only pattern is
%e .X
%e XX
%e a(9) = 50, with a similar pattern to prove that r >= 2/3:
%e X.......X
%e .XXXXXXX.
%e X.......X
%e .........
%e XXXXXXXXX
%e .........
%e X.......X
%e .XXXXXXX.
%e X.......X
%e a(10) = 61, and a pattern that reaches that is
%e X..X...X..
%e XX.X.X.X.X
%e ..........
%e .X.XX.X.XX
%e XX....X...
%e ....X....X
%e X.XX..XX.X
%e X....X....
%e ...X....XX
%e XX.X.XX.X.
%Y If we only want 1 marked neighbor, we get n^2 - A075561(n).
%K nonn,hard,more
%O 1,3
%A _Tomas Rigaux_, Apr 04 2023