A396207 Number of relations R on an n-element set such that the transitive closure of R has exactly seven elements more than R.

0, 0, 0, 0, 7020, 2623730, 772712220, 304370184244

Offset

0,5

Comments

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.

Links

Table of n, a(n) for n=0..7.

Example

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)}.

Crossrefs

Cf. A006905, A395083, A395919, A395920.

Sequence in context: A100897 A206757 A236061 * A317399 A116278 A206050

Adjacent sequences: A396204 A396205 A396206 * A396208 A396209 A396210

Keyword

nonn,hard,more

Author

Firdous Ahmad Mala, May 18 2026

Status

approved