A393191 Number of purely (not vacuously) transitive relations on an n-set.

0, 0, 1, 67, 2602, 127391, 8670037, 849052226, 120598537031, 24766028284955, 7293869441425936, 3051443919384918993, 1796556570870581636365, 1475927350935844025485280, 1679181820016034990525166005, 2628190444358197603661882875487, 5626146387384970881514304524196922

Offset

0,4

Comments

This sequence counts the number of transitive relations that are not vacuous.

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = A006905(n) - A391878(n).

Example

a(2)=1 because on a 2-set {x,y}, R={(x,y),(y,x),(x,x),(y,y)} is the only transitive relation that is not vacuous.

Crossrefs

Cf. A006905, A391878, A003041.

Sequence in context: A078953 A226713 A069397 * A103727 A120663 A261974

Adjacent sequences: A393188 A393189 A393190 * A393192 A393193 A393194

Keyword

nonn

Author

Firdous Ahmad Mala, Feb 04 2026

Status

approved