A396053 - OEIS

%I #11 May 20 2026 17:57:35

%S 0,0,0,39,8631,1269960,240203160

%N Number of relations R on an n-element set such that the transitive closure of R has exactly four elements more than R.

%C Equivalently, a(n) is the number of binary relations R on an n-set for which exactly four ordered pairs must be adjoined to obtain a transitive relation; i.e., |closure(R) \ R| = 4.

%e For n = 0, 1 every relation is transitive, so a(0) = a(1) = 0.

%e For n = 3, one of the a(3) = 39 relations is R = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1)}, whose transitive closure R = [3] X [3] adds exactly the four pairs (2, 2), (2, 3), (3, 2), (3, 3).

%Y Cf. A006905, A395083, A395919, A395920.

%K nonn,hard,more

%O 0,4

%A _Firdous Ahmad Mala_, May 14 2026

%E a(6) from _Christian Sievers_, May 20 2026