A382839 Number of dense binary relations on {1,...,n}.

1, 2, 7, 114, 9602, 3962940, 7516789560, 62622777447552, 2221417812173570640

Offset

0,2

Comments

A binary relation R is usually called dense if for all R-related x and y there exists z such that x and z and also z and y are R-related (see Wikipedia link), but here we define a binary relation R on {1,...,n} to be "dense" (see the second page of the paper in the links) iff for all x and y we have (zRx implies zRy for all z) implies (x <= y).

Equivalently, as mentioned in a SeqFan post (see link), for all x < y, some z satisfies (not zRx) AND zRy.

Brendan McKay added terms for n = 6 and 7 in a SeqFan post (see link).

Links

Table of n, a(n) for n=0..8.

Francesco Ciraulo and Giovanni Sambin, The overlap algebra of regular opens, Journal of Pure and Applied Algebra, Volume 214, Issue 11, November 2010, Pages 1988-1995.

Seqfan, number of dense symmetric binary relations on {1,...,n} (A382693) and also.

Wikipedia, Dense Order, Generalizations.

Crossrefs

Cf. A382693 (without symmetry).

Sequence in context: A326940 A326964 A034902 * A101429 A270749 A206151

Adjacent sequences: A382836 A382837 A382838 * A382840 A382841 A382842

Keyword

nonn,more

Author

Mark Bowron, Apr 06 2025

Extensions

a(8) from Christian Sievers, May 26 2025

Status

approved