

A350237


Minimum number of 1's in an n X n binary matrix with no zero 3 X 3 submatrix.


11



0, 0, 1, 3, 5, 10, 16, 22, 32, 40, 52, 64, 77, 91, 105, 128
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OFFSET

1,4


COMMENTS

The submatrix's rows and columns need not be contiguous, so the following matrix does not show a(4) = 1:
....
.1..
....
....


LINKS



FORMULA



EXAMPLE

a(4) = 3 because the following 4 X 4 binary matrix with 3 1's has no zero 3 X 3 submatrix, and all such matrices with fewer 1's have at least one zero 3 X 3 submatrix:
1...
.1..
..1.
....


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



