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A003087 Number of acyclic digraphs with n unlabeled nodes.
(Formerly M1696)
1, 1, 2, 6, 31, 302, 5984, 243668, 20286025, 3424938010, 1165948612902, 797561675349580, 1094026876269892596, 3005847365735456265830, 16530851611091131512031070, 181908117707763484218885361402 (list; graph; refs; listen; history; text; internal format)



Also the number of equivalence classes of n X n real (0,1)-matrices with all eigenvalues positive, up to conjugation by permutations.


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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


R. W. Robinson and Sean A. Irvine, Table of n, a(n) for n = 0..36 [Terms 0 through 18 were computed by R. W. Robinson; terms 19 through 36 by Sean A. Irvine, Jan 22 2014]

Jack Kuipers and Giusi Moffa, Uniform generation of random acyclic digraphs, arXiv preprint arXiv:1202.6590, 2012. - N. J. A. Sloane, Sep 14 2012

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, arXiv:math/0310423 [math.CO], 2003.

Lawrence Ong, Optimal Finite-Length and Asymptotic Index Codes for Five or Fewer Receivers, arXiv preprint arXiv:1606.05982 [cs.IT], 2016.

R. W. Robinson, Enumeration of acyclic digraphs, Manuscript. (Annotated scanned copy)

Eric Weisstein's World of Mathematics, Acyclic Digraph.

Index entries for sequences related to binary matrices


Cf. A003024 (the labeled case), A082402. Rows sums of A122078.

Sequence in context: A018225 A217143 A075845 * A203901 A190958 A109243

Adjacent sequences:  A003084 A003085 A003086 * A003088 A003089 A003090




N. J. A. Sloane



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Last modified March 17 18:39 EDT 2018. Contains 300573 sequences. (Running on oeis4.)