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A005019
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The number of n X n (0,1)-matrices with a 1-width of 1.
(Formerly M4461)
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0
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1, 7, 169, 14911, 4925281, 6195974527, 30074093255809, 568640725896660991, 42170765737391337500161, 12325140160135610565932361727, 14244006984657003076298588475598849
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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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]
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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