A003041 Number of vacuously transitive relations on n nodes up to isomorphism. (Formerly M1764)

2, 7, 24, 92, 388

Offset

1,1

Comments

A transitive relation is vacuously transitive if it does not contain any transitive triple, that is, three distinct ordered pairs (a,b), (b,c), (a,c). - Jukka Kohonen, Sep 17 2021

References

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

Links

Table of n, a(n) for n=1..5.

H. Sharp, Jr., Enumeration of vacuously transitive relations, Discrete Math. 4 (1973), 185-196.

Example

a(2)=7: The seven relations are {}, {(1,1)}, {(1,1),(2,2)}, {(2,1)}, {(1,1),(2,1)}, {(1,1),(2,1),(2,2)} and {(2,1),(2,2)}. - Jukka Kohonen, Sep 17 2021

Crossrefs

Cf. A347700, A348240.

Sequence in context: A150399 A150400 A150401 * A026558 A150402 A151295

Adjacent sequences: A003038 A003039 A003040 * A003042 A003043 A003044

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Clarified and offset corrected by Jukka Kohonen, Sep 17 2021

Status

approved