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

1, 7, 169, 14911, 4925281, 6195974527, 30074093255809, 568640725896660991, 42170765737391337500161, 12325140160135610565932361727, 14244006984657003076298588475598849

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

Examples

			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
		

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

• Index entries for sequences related to binary matrices

Crossrefs

a(n) = 2^(n^2)- A055601. - Geoffrey Critzer, Dec 03 2009

Cf. A005020 (1-width of 2).

Programs

Mathematica

Table[2^(n^2) - (2^n - 1)^n, {n, 1, 15}] (* Geoffrey Critzer, Dec 03 2009 *)

Formula

a(n) = 2^(n^2) - ((2^n)-1)^n. - Geoffrey Critzer, Mar 01 2009

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