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%I #18 Mar 14 2023 09:50:50
%S 0,2,6,8,12,14,18,22,26,32,36,42,48,54,60,66,72,78,84,92,100,104,112,
%T 118,126,134,142,152,160,170,180,184,192,204,212,220,226,234,244,254
%N A problem of Zarankiewicz: maximal number of 1's in a symmetric n X n matrix of 0's and 1's with 0's on the main diagonal and no "rectangle" with 1's at the four corners.
%C In other words, the pattern
%C 1...1
%C .....
%C 1...1
%C is forbidden.
%C Such matrices are adjacency matrices of squarefree graphs (cf. A006786). The number of matrices with a(n) ones is given by A191966 and A335820 (up to permutations of rows/columns). - _Max Alekseyev_, Jan 29 2022
%D B. Bollobas, Extremal Graph Theory, pp. 309ff.
%H D. Bienstock E. Gyori, <a href="https://epubs.siam.org/doi/pdf/10.1137/0404002">An extremal problem on sparse 0-1 matrices</a>. SIAM J. Discrete Math. 4 (1991), 17-27.
%F a(n) = 2 * A006855(n). - _Max Alekseyev_, Jan 29 2022
%Y Cf. A006786, A006855, A077269, A191873 A191874, A191966, A300756, A335820, A352472.
%K nonn,more
%O 1,2
%A _R. H. Hardin_ and _N. J. A. Sloane_, Jun 18 2011
%E a(11)-a(40) computed from A006855 by _Max Alekseyev_, Jan 28 2022; Apr 2, 2022; Mar 14 2023
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