cp's OEIS Frontend

A005019 The number of n X n (0,1)-matrices with a 1-width of 1.

%I A005019 M4461 #20 Mar 06 2020 22:37:07
%S A005019 1,7,169,14911,4925281,6195974527,30074093255809,568640725896660991,
%T A005019 42170765737391337500161,12325140160135610565932361727,
%U A005019 14244006984657003076298588475598849
%N A005019 The number of n X n (0,1)-matrices with a 1-width of 1.
%C A005019 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
%C A005019 a(n) is the number of n X n binary matrices with at least one row of 0's. - _Geoffrey Critzer_, Dec 03 2009
%D A005019 Lam, Clement W. H., The distribution of 1-widths of (0, 1)-matrices. Discrete Math. 20 (1977/78), no. 2, 109-122.
%D A005019 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A005019 Stanley, Enumerative Combinatorics, Volume I, Example 1.1.16 [From _Geoffrey Critzer_, Dec 03 2009]
%H A005019 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F A005019 a(n) = 2^(n^2) - ((2^n)-1)^n. - _Geoffrey Critzer_, Mar 01 2009
%e A005019 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
%t A005019 Table[2^(n^2) - (2^n - 1)^n, {n, 1, 15}] (* _Geoffrey Critzer_, Dec 03 2009 *)
%Y A005019 a(n) = 2^(n^2)- A055601. - _Geoffrey Critzer_, Dec 03 2009
%Y A005019 Cf. A005020 (1-width of 2).
%K A005019 nonn
%O A005019 1,2
%A A005019 _N. J. A. Sloane_
%E A005019 a(7) from _Geoffrey Critzer_, Mar 01 2009
%E A005019 More terms from _Geoffrey Critzer_, Dec 03 2009
%E A005019 Title improved by _Sean A. Irvine_, Mar 06 2020