Search: id:A003087
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%I A003087 M1696
%S A003087 1,1,2,6,31,302,5984,243668,20286025,3424938010,1165948612902,
%T A003087 797561675349580,1094026876269892596,3005847365735456265830,
%U A003087 16530851611091131512031070,181908117707763484218885361402
%N A003087 Number of acyclic digraphs with n unlabeled nodes.
%C A003087 Also the number of equivalence classes of n X n real (0,1)-matrices with 
               all eigenvalues positive, up to conjugation by permutations.
%D A003087 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003087 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 194.
%D A003087 R. W. Robinson, Counting unlabeled acyclic digraphs, in "Combinatorial 
               Mathematics V (Melbourne 1976)", Lect. Notes Math. 622 (1976), pp. 
               28-43.
%D A003087 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%H A003087 R. W. Robinson, <a href="b003087.txt">Table of n, a(n) for n = 0..18</
               a>
%H A003087 B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless 
               and H. S. Wilf, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">Acyclic digraphs and eigenvalues of (0,1)-matrices</a>
               , J. Integer Sequences, 7 (2004), #04.3.3.
%H A003087 B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless 
               and H. S. Wilf, <a href="http://arXiv.org/abs/math.CO/0310423">Acyclic 
               digraphs and eigenvalues of (0,1)-matrices</a>
%H A003087 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AcyclicDigraph.html">Link to a section of The World of Mathematics.</
               a>
%H A003087 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%Y A003087 Cf. A003024 (the labeled case), A082402. Rows sums of A122078.
%Y A003087 Sequence in context: A113719 A018225 A075845 this_sequence A109243 A108327 
               A121071
%Y A003087 Adjacent sequences: A003084 A003085 A003086 this_sequence A003088 A003089 
               A003090
%K A003087 nonn,nice
%O A003087 0,3
%A A003087 N. J. A. Sloane (njas(AT)research.att.com).

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