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.
%I A347472 #19 Feb 08 2022 17:59:27
%S A347472 0,2,6,12,19,27,39,51,65,81,98,116,139,163,188,214,242,272,303,335,
%T A347472 375,413,453
%N A347472 Maximum number of nonzero entries allowed in an n X n matrix to ensure there is a 2 X 2 zero submatrix.
%C A347472 Related to Zarankiewicz's problem k_2(n) (cf. A001197 and other crossrefs) which asks the converse: how many 1's must be in an n X n {0,1}-matrix in order to guarantee the existence of an all-ones 2 X 2 submatrix. This complementarity leads to the given formula which was used to compute the given values.
%C A347472 See A347473 and A347474 for the similar problem with a 3 X 3 resp. 4 X 4 zero submatrix.
%F A347472 a(n) = n^2 - A001197(n).
%F A347472 a(n) = A350296(n) - 1. - _Andrew Howroyd_, Dec 23 2021
%e A347472 For n = 2, there must not be any nonzero entry in an n X n = 2 X 2 matrix, if one wants a 2 X 2 zero submatrix, whence a(2) = 0.
%e A347472 For n = 3, having at most 2 nonzero entries in the n X n matrix still guarantees that there is a 2 X 2 zero submatrix (delete the row of the first nonzero entry and then the column of the remaining nonzero entry, if any), but if one allows 3 nonzero entries and they are placed on the diagonal, then there is no 2 X 2 zero submatrix. Hence, a(3) = 2.
%Y A347472 Cf. A001197 (k_2(n)), A001198 (k_3(n)), A006613 - A006626.
%Y A347472 Cf. A347473, A347474 (analog for 3 X 3 resp. 4 X 4 zero submatrix).
%Y A347472 Cf. A350296.
%K A347472 nonn,hard,more
%O A347472 2,2
%A A347472 _M. F. Hasler_, Sep 28 2021
%E A347472 a(22)-a(24) computed from A001197 by _Max Alekseyev_, Feb 08 2022