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A362016
Maximal number of unmarked cells with at least 3 marked neighboring cells in the n X n kings' graph.
1
0, 1, 4, 8, 13, 20, 28, 38, 50, 61, 75, 90, 108, 124, 139
OFFSET
1,3
COMMENTS
The value of r = lim sup a(n) / n^2 is in the half-open interval [2/3, 8/11).
It appears from the computed terms that r = 2/3.
EXAMPLE
a(2) = 1, as the only pattern is
.X
XX
a(9) = 50, with a similar pattern to prove that r >= 2/3:
X.......X
.XXXXXXX.
X.......X
.........
XXXXXXXXX
.........
X.......X
.XXXXXXX.
X.......X
a(10) = 61, and a pattern that reaches that is
X..X...X..
XX.X.X.X.X
..........
.X.XX.X.XX
XX....X...
....X....X
X.XX..XX.X
X....X....
...X....XX
XX.X.XX.X.
CROSSREFS
If we only want 1 marked neighbor, we get n^2 - A075561(n).
Sequence in context: A056738 A170907 A143978 * A071994 A023661 A157130
KEYWORD
nonn,hard,more
AUTHOR
Tomas Rigaux, Apr 04 2023
STATUS
approved