A395715 Number of relations on an n-set that are reflexive and transitive, but not symmetric.

0, 0, 2, 24, 340, 6890, 209324, 9534364, 642775214, 63260268276, 8977053757068, 1816846038057622, 519355571061560424, 207881393656641308604, 115617051977054076908138, 88736269118586243109526576, 93411113411710039554730351948, 134137950093337880672239003856042, 261492535743634374805065444824311044

Offset

0,3

Comments

Equivalently, a(n) is the number of preorders (quasi-orders) on a labeled n-set that are not equivalence relations.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = A000798(n) - A000110(n).

Example

For n=2 the a(2)=2 preorders that are not equivalence relations are the two total orders {(1,1),(2,2),(1,2)} and {(1,1),(2,2),(2,1)}.

Crossrefs

Cf. A000798, A000110, A001035, A202534, A005493, A394620.

Sequence in context: A333715 A081065 A262291 * A043699 A220317 A220340

Adjacent sequences: A395712 A395713 A395714 * A395716 A395717 A395720

Keyword

nonn

Author

Firdous Ahmad Mala, May 04 2026

Status

approved