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 A001197 M3300 N1330 #55 Sep 14 2024 16:46:24 %S A001197 4,7,10,13,17,22,25,30,35,40,46,53,57,62,68,75,82,89,97,106,109,116, %T A001197 123 %N A001197 Zarankiewicz's problem k_2(n). %C A001197 a(n) is the minimum number k_2(n) such that any n X n matrix having that number of nonzero entries has a 2 X 2 submatrix with only nonzero entries. - _M. F. Hasler_, Sep 28 2021 %C A001197 a(n) <= (1 + sqrt(4*n-3))*n/2 + 1. - _Max Alekseyev_, Apr 03 2022 %D A001197 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 291. %D A001197 R. K. Guy, A problem of Zarankiewicz, in P. Erdős and G. Katona, editors, Theory of Graphs (Proceedings of the Colloquium, Tihany, Hungary), Academic Press, NY, 1968, pp. 119-150. %D A001197 Richard J. Nowakowski, Zarankiewicz's Problem, PhD Dissertation, University of Calgary, 1978, page 202. %D A001197 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A001197 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A001197 R. K. Guy, <a href="/A001197/a001197.pdf">A problem of Zarankiewicz</a>, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. [Annotated and scanned copy, with permission] %H A001197 R. K. Guy, <a href="http://dx.doi.org/10.1007/BFb0060112">A many-facetted problem of Zarankiewicz</a>, Lect. Notes Math. 110 (1969), 129-148. %F A001197 a(n) = A072567(n) + 1. - _Rob Pratt_, Aug 09 2019 %F A001197 a(n) = n^2 - A347472(n) = n^2 - A350296(n) + 1. - _Andrew Howroyd_, Dec 26 2021 %Y A001197 Cf. A001198 (k_3), A072567, A339635, A347472, A350296. %Y A001197 Cf. also A006613 - A006626 (other sizes, in particular A006616 = k_4). %Y A001197 Main diagonal of A376167. %K A001197 nonn,hard,more %O A001197 2,1 %A A001197 _N. J. A. Sloane_ %E A001197 Nowakowski's thesis, directed by Guy, corrected Guy's value for a(15) and supplied a(16)-a(21) entered by _Don Knuth_, Aug 13 2014 %E A001197 a(1) deleted following a suggestion from _M. F. Hasler_. - _N. J. A. Sloane_, Oct 22 2021 %E A001197 a(22)-a(24) from _Jeremy Tan_, Jan 23 2022