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

Offset

0,3

Comments

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

References

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).

Links

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.

Index entries for sequences related to binary matrices

Crossrefs

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

Adjacent sequences: A003084 A003085 A003086 * A003088 A003089 A003090

Keyword

nonn,nice

Author

N. J. A. Sloane

Status

approved