A003041 Number of vacuously transitive relations on n nodes up to isomorphism.

2, 7, 24, 92, 388

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

Examples

			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
		

References

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

Links

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

Crossrefs

Cf. A347700, A348240.

Extensions

Clarified and offset corrected by Jukka Kohonen, Sep 17 2021