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 A005019 The number of n X n (0,1)-matrices with a 1-width of 1. (Formerly M4461) 0
 1, 7, 169, 14911, 4925281, 6195974527, 30074093255809, 568640725896660991, 42170765737391337500161, 12325140160135610565932361727, 14244006984657003076298588475598849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of ways to linearly order (with repetition allowed) n subsets of {1,2,...n} so that the generalized intersection of the subsets is not empty. - Geoffrey Critzer, Mar 01 2009 a(n) is the number of n X n binary matrices with at least one row of 0's. - Geoffrey Critzer, Dec 03 2009 REFERENCES Lam, Clement W. H., The distribution of 1-widths of (0, 1)-matrices. Discrete Math. 20 (1977/78), no. 2, 109-122. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). Stanley, Enumerative Combinatorics, Volume I, Example 1.1.16 [From Geoffrey Critzer, Dec 03 2009] LINKS FORMULA a(n) = 2^(n^2) - ((2^n)-1)^n. - Geoffrey Critzer, Mar 01 2009 EXAMPLE a(2)=7 because there are seven ways to order two subsets of {1,2} so that the intersection of the subsets contains at least one element: {1}{1};{1}{1,2};{2}{2};{2}{1,2};{1,2}{1};{1,2}{2};{1,2}{1,2}. - Geoffrey Critzer, Mar 01 2009 MATHEMATICA Table[2^(n^2) - (2^n - 1)^n, {n, 1, 15}] (* Geoffrey Critzer, Dec 03 2009 *) CROSSREFS a(n) = 2^(n^2)- A055601. - Geoffrey Critzer, Dec 03 2009 Cf. A005020 (1-width of 2). Sequence in context: A258299 A012067 A012145 * A172027 A113562 A157203 Adjacent sequences:  A005016 A005017 A005018 * A005020 A005021 A005022 KEYWORD nonn AUTHOR EXTENSIONS a(7) from Geoffrey Critzer, Mar 01 2009 More terms from Geoffrey Critzer, Dec 03 2009 Title improved by Sean A. Irvine, Mar 06 2020 STATUS approved

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Last modified May 13 05:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)