A396053 Number of relations R on an n-element set such that the transitive closure of R has exactly four elements more than R.

0, 0, 0, 39, 8631, 1269960, 240203160

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..6.

Example

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

Crossrefs

Cf. A006905, A395083, A395919, A395920.

Sequence in context: A266453 A279116 A266307 * A210327 A174765 A115462

Adjacent sequences: A396049 A396050 A396052 * A396054 A396055 A396056

Keyword

nonn,hard,more

Author

Firdous Ahmad Mala, May 14 2026

Extensions

a(6) from Christian Sievers, May 20 2026

Status

approved