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A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 2 X 2 submatrix.
(Formerly M3775)
6

%I M3775 #23 Mar 22 2024 18:02:30

%S 5,8,11,15,19,23,27,32,37,43,49,54,59,64

%N A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 2 X 2 submatrix.

%C a(n) <= A205805(2*n+1) + 1. - _Max Alekseyev_, Feb 02 2024

%D R. K. Guy, A many-facetted problem of Zarankiewicz, Lect. Notes Math. 110 (1969), 129-148.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%Y Cf. A006613, A006614, A006615, A006616, A006617, A006618, A006619, A006621, A006622, A006623, A006624, A006625, A006626.

%Y Cf. A001197, A072567, A191965, A191873, A001198, A205805, A347473, A347474, A350304, A350237.

%K nonn,more

%O 2,1

%A _N. J. A. Sloane_

%E Name changed at the suggestion of _Sean A. Irvine_ by _Max Alekseyev_, Feb 02 2024

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Last modified September 21 20:27 EDT 2024. Contains 376089 sequences. (Running on oeis4.)