A396220 - OEIS

%I #9 May 25 2026 18:01:05

%S 0,0,0,0,4719,3183890,1078414245

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

%C Equivalently, a(n) is the number of binary relations R on an n-set for which exactly eight ordered pairs must be adjoined to obtain a transitive relation; i.e., |closure(R) \ R| = 8.

%e For n <= 3 we have n^2 <= 9, so a relation differing from its closure by eight pairs would have to be empty with full closure, which is impossible. Hence a(0) = a(1) = a(2) = a(3) = 0.

%Y Cf. A006905, A395083, A395919, A395920, A396053, A396054, A396055.

%K nonn,hard,more

%O 0,5

%A _Firdous Ahmad Mala_, May 19 2026