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 A350237 Minimum number of 1's in an n X n binary matrix with no zero 3 X 3 submatrix. 11
 0, 0, 1, 3, 5, 10, 16, 22, 32, 40, 52, 64, 77, 91, 105, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The submatrix's rows and columns need not be contiguous, so the following matrix does not show a(4) = 1: .... .1.. .... .... LINKS Table of n, a(n) for n=1..16. Jeremy Tan, Python program with illustration of initial terms Jeremy Tan, Two genies and their kind of chess, Puzzling Stack Exchange, Dec 19 2021. (shows a(8) = 22) Jeremy Tan, What's the minimum number of people required?, Mathematics Stack Exchange, Dec 20 2021. Jeremy Tan, An attack on Zarankiewicz's problem through SAT solving, arXiv:2203.02283 [math.CO], 2022. FORMULA a(n) = A347473(n) + 1 = n^2 - A001198(n) + 1. a(n) = n^2 - A350304(n). - Max Alekseyev, Oct 31 2022 EXAMPLE a(4) = 3 because the following 4 X 4 binary matrix with 3 1's has no zero 3 X 3 submatrix, and all such matrices with fewer 1's have at least one zero 3 X 3 submatrix: 1... .1.. ..1. .... CROSSREFS Column 3 of A339635. Cf. A001198, A347473, A350304. Sequence in context: A358406 A287563 A184800 * A267151 A209008 A032279 Adjacent sequences: A350234 A350235 A350236 * A350238 A350239 A350240 KEYWORD nonn,hard,more AUTHOR Jeremy Tan, Dec 21 2021 EXTENSIONS a(12)-a(13) from Andrew Howroyd, Dec 23 2021 a(14)-a(15) from Jeremy Tan, Jan 03 2022 a(16) from Jeremy Tan, added by Max Alekseyev, Oct 31 2022 STATUS approved

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Last modified August 9 20:04 EDT 2024. Contains 375044 sequences. (Running on oeis4.)