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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, 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).
Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 0..18 were computed by R. W. Robinson; terms 19..36 by Sean A. Irvine, Jan 22 2014)
Jack Kuipers and Giusi Moffa, Uniform generation of random acyclic digraphs, arXiv preprint arXiv:1202.6590 [stat.CO], 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, Counting unlabeled acyclic digraphs, in Little C.H.C. (Ed.), "Combinatorial Mathematics V (Melbourne 1976)", Lect. Notes Math. 622 (1976), pp. 28-43. DOI:10.1007/BFb0069178.
R. W. Robinson, Enumeration of acyclic digraphs, Manuscript. (Annotated scanned copy)
Eric Weisstein's World of Mathematics, Acyclic Digraph.
Cf. A003024 (the labeled case), A082402, A101228 (weakly connected, inverse Euler Trans).
Rows sums of A122078, A350447, A350448.
Sequence in context: A018225 A217143 A075845 * A203901 A342396 A190958

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Last modified November 29 07:51 EST 2023. Contains 367429 sequences. (Running on oeis4.)