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Search: id:A003087
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| A003087 |
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Number of acyclic digraphs with n unlabeled nodes.
(Formerly M1696)
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+0
6
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| 1, 1, 2, 6, 31, 302, 5984, 243668, 20286025, 3424938010, 1165948612902, 797561675349580, 1094026876269892596, 3005847365735456265830, 16530851611091131512031070, 181908117707763484218885361402
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also the number of equivalence classes of n X n real (0,1)-matrices with all eigenvalues positive, up to conjugation by permutations.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 194.
R. W. Robinson, Counting unlabeled acyclic digraphs, in "Combinatorial Mathematics V (Melbourne 1976)", Lect. Notes Math. 622 (1976), pp. 28-43.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
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LINKS
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R. W. Robinson, Table of n, a(n) for n = 0..18
B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices, J. Integer Sequences, 7 (2004), #04.3.3.
B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to binary matrices
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CROSSREFS
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Cf. A003024 (the labeled case), A082402. Rows sums of A122078.
Sequence in context: A113719 A018225 A075845 this_sequence A109243 A108327 A121071
Adjacent sequences: A003084 A003085 A003086 this_sequence A003088 A003089 A003090
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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