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A005019
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(0,1)-matrices by 1-width.
(Formerly M4461)
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0
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1, 7, 169, 14911, 4925281, 6195974527, 30074093255809, 568640725896660991, 42170765737391337500161, 12325140160135610565932361727, 14244006984657003076298588475598849
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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. [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]
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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 (critzer.geoffrey(AT)usd443.org), Dec 03 2009]
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LINKS
| Index entries for sequences related to binary matrices
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FORMULA
| a(n)=2^(n^2)-[(2^n)-1]^n [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 01 2009]
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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} [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 01 2009]
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MATHEMATICA
| Table[2^(n^2) - (2^n - 1)^n, {n, 1, 15}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009]
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CROSSREFS
| a(n) = 2^(n^2)- A055601 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 03 2009]
Sequence in context: A162131 A012067 A012145 * A172027 A113562 A157203
Adjacent sequences: A005016 A005017 A005018 * A005020 A005021 A005022
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| 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
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