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%I #9 May 24 2026 18:02:07
%S 0,0,0,0,7020,2623730,772712220,304370184244
%N Number of relations R on an n-element set such that the transitive closure of R has exactly seven elements more than R.
%C Equivalently, a(n) is the number of binary relations R on an n-set for which exactly seven ordered pairs must be adjoined to obtain a transitive relation; i.e., |closure(R) \ R| = 7.
%e For n = 4, one of the a(4) = 7020 relations on {1, 2, 3, 4} that requires exactly seven new pairs to become transitive is R = {(1, 2), (1, 3), (1, 4), (2, 1), (3, 1)}. Its transitive closure adds the seven pairs {(1, 1), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}.
%Y Cf. A006905, A395083, A395919, A395920.
%K nonn,hard,more
%O 0,5
%A _Firdous Ahmad Mala_, May 18 2026