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A350304
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Maximum number of 1's in an n X n binary matrix without an all-ones 3 X 3 submatrix.
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9
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1, 4, 8, 13, 20, 26, 33, 42, 49, 60, 69, 80, 92, 105, 120, 128
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OFFSET
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1,2
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COMMENTS
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Equivalently, the maximum number of edges in a bipartite graph that is a subgraph of K_{n,n} and has no K_{3,3} induced subgraph.
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REFERENCES
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W. Sierpiński, Sur un problème concernant un réseau à 36 points, Ann. Soc. Polon. Math., 24: 173-174 (1951).
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LINKS
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FORMULA
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EXAMPLE
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Examples of a(3)=8, a(4)=13, a(5)=20, a(6)=26:
x x x x x x x x x x x . x x x x x .
x x x x x x . x x x . x x x x x . x
x x . x x . x x x . x x x x . . x x
x . x x x . x x x x . x . x x
. x x x x . x . x x x
. . x x x x
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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