cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A350304 Maximum number of 1's in an n X n binary matrix without an all-ones 3 X 3 submatrix.

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%I A350304 #24 Oct 31 2022 09:35:46
%S A350304 1,4,8,13,20,26,33,42,49,60,69,80,92,105,120,128
%N A350304 Maximum number of 1's in an n X n binary matrix without an all-ones 3 X 3 submatrix.
%C A350304 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.
%D A350304 W. Sierpiński, Sur un problème concernant un réseau à 36 points, Ann. Soc. Polon. Math., 24: 173-174 (1951).
%H A350304 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zarankiewicz_problem">Zarankiewicz problem</a>
%F A350304 a(n) = A001198(n) - 1 = n^2 - A350237(n) = n^2 - A347473(n) - 1.
%e A350304 Examples of a(3)=8, a(4)=13, a(5)=20, a(6)=26:
%e A350304   x x x    x x x x    x x x x .    x x x x x .
%e A350304   x x x    x x x .    x x x . x    x x x x . x
%e A350304   x x .    x x . x    x x . x x    x x . . x x
%e A350304            x . x x    x . x x x    x . x . x x
%e A350304                       . x x x x    . x . x x x
%e A350304                                    . . x x x x
%Y A350304 Cf. A001198, A072567, A339635, A347473, A350237.
%K A350304 nonn,more
%O A350304 1,2
%A A350304 _Andrew Howroyd_, Dec 24 2021
%E A350304 a(14)-a(16) computed from A350237 by _Max Alekseyev_, Apr 01 2022, Oct 31 2022