A006057 -id:A006057 - cp's OEIS frontend

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

Jonathan Vos Post, Feb 16 2010

Previous name was: Partial sums of A000112.

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.

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

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

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

New name from Geoffrey Critzer, May 22 2022

A173399 Partial sums of A000798.

Original entry on oeis.org

1, 2, 6, 35, 390, 7332, 216859, 9752100, 652531454, 63912820877, 9040966693920, 1825887005430112, 521181458071204133, 208402575114740157174, 115825454552169007964634, 88852094573138413500449755, 93499965506283177978710943850, 134231450058844163850300579669696, 261626767193693218968916427480786899

Offset: 0

Jonathan Vos Post, Feb 17 2010

nonn

Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements.

The subsequence of primes in this partial sum begins: 2, 216859.

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

Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {, }][[All, 2]] // Accumulate (* Jean-François Alcover, Dec 30 2019 *)

a(n) = Sum_{i=0..n} A000798(i).

Missing term 7332 added and extended by Jean-François Alcover, Dec 30 2019

cp's OEIS Frontend

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

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