A173311 a(n) is the number of regular D classes in the semigroup of all binary relations on [n].

1, 2, 4, 9, 25, 88, 406, 2451, 19450, 202681, 2769965, 49519392, 1154411138, 34978238590, 1373171398361, 69648249299517, 4552778914494604

Offset

0,2

Comments

Previous name was: Partial sums of A000112.

Links

Table of n, a(n) for n=0..16.

K. K.-H. Butler and G. Markowsky, The Number of Maximal Subgroups of the Semigroup of Binary Relations, Kyungpook Math. J. Vol 12, June 1972.

Formula

a(n) = Sum_{i=0..n} A000112(i).

Mathematica

Cases[Import["https://oeis.org/A000112/b000112.txt", "Table"], {_, _}][[All, 2]] // Accumulate (* Jean-François Alcover, Jan 01 2020 *)

Crossrefs

Cf. A000112, A000798 (labeled topologies), A001035 (labeled posets), A001930 (unlabeled topologies), A006057, A079263, A079265, A007903.

Sequence in context: A192801 A270954 A173496 * A127055 A124835 A125799

Adjacent sequences: A173308 A173309 A173310 * A173312 A173313 A173314

Keyword

nonn,hard,more

Author

Jonathan Vos Post, Feb 16 2010

Extensions

New name from Geoffrey Critzer, May 22 2022

Status

approved