A394405 - OEIS

%I #9 Mar 23 2026 22:02:08

%S 0,1,9,142,3639,147361,9205662,868687289,121564924269,24827487632524,

%T 7298473245637245,3051704700294366865,1796484203652704550216,

%U 1475854812473362457120271,1679123941097593174888995537,2628136437874738720379203091550,5626082456400367348667440806098859

%N Number of transitive relations, on an n-set, that are not quasi-orders.

%C A quasi-order is a relation that is both transitive and reflexive.

%C a(n) is the number by which the number of transitive relations exceeds the number of quasi-orders.

%F a(n) = A006905(n) - A000798(n).

%e On a 1-set, X={x}, the only relation that is transitive but not reflexive (or a quasi-order) is the empty relation, thus, a(1)=1.

%Y Cf. A000798, A006905.

%K nonn,hard

%O 0,3

%A _Firdous Ahmad Mala_, Mar 19 2026