1,2

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. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 01 2009]

a(n) is the number of n X n binary matrices with at least one row of 0's. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009]

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

Lam, Clement W. H. The distribution of $1$-widths of $(0, 1)$-matrices. Discrete Math. 20 (1977/78), no. 2, 109-122.

Stanley, Enumerative Combinatorics, Volume I, Example 1.1.16 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009]

Index entries for sequences related to binary matrices

a(n)=2^(n^2)-[(2^n)-1]^n [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 01 2009]

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} [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 01 2009]

Table[2^(n^2) - (2^n - 1)^n, {n, 1, 15}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009]

Sequence in context: A162131 A012067 A012145 this_sequence A113562 A157203 A075599

Adjacent sequences: A005016 A005017 A005018 this_sequence A005020 A005021 A005022

a(n) = 2^(n^2)- A055601 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009]

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).

Added a(7) Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 01 2009

More terms from Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009