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Search: id:A055165
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| A055165 |
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Number of regular n X n matrices with rational entries equal to 0 or 1. |
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+0
18
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| 1, 6, 174, 22560, 12514320, 28836612000, 270345669985440, 10160459763342013440
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All eigenvalues are nonzero.
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REFERENCES
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Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Miodrag Zivkovic, More information
Index entries for sequences related to binary matrices
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FORMULA
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For an asymptotic estimate see A046747. A002884 is a lower bound. A002416 is an upper bound.
a(n) = n! * A088389(n) - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 20 2007
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EXAMPLE
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For n=2 the 6 matrices are {{{0, 1}, {1, 0}}, {{0, 1}, {1, 1}}, {{1, 0}, {0, 1}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}, {{1, 1}, {1, 0}}}.
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CROSSREFS
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Cf. A056990, A056989, A046747, A055165, A002416, A003024 (positive definite matrices).
A046747(n) + a(n) = 2^(n^2) = total number of n X n (0, 1) matrices = sequence A002416.
Sequence in context: A106661 A003720 A002884 this_sequence A071095 A134632 A024277
Adjacent sequences: A055162 A055163 A055164 this_sequence A055166 A055167 A055168
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KEYWORD
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nonn,nice,hard
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AUTHOR
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Ulrich Hermisson (uhermiss(AT)server1.rz.uni-leipzig.de), Jun 18 2000
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EXTENSIONS
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More terms from MIodrag Zivkovic (ezivkovm(AT)matf.bg.ac.yu), Feb 28 2006
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