A060639 -id:A060639 - cp's OEIS frontend

A318395 Number of nonnegative integer matrices with values summing to n, up to transposition and permutation of rows and columns.

1, 1, 3, 7, 21, 54, 167, 491, 1586, 5132, 17442, 60399, 216172, 790436, 2965333, 11365813, 44536775, 178107679, 726716229, 3022464373, 12807206008, 55253891494, 242585471236, 1083255591604, 4917631017573, 22685090928596, 106291554085987, 505653658171936, 2441383079595849

Offset: 0

Gus Wiseman, Aug 25 2018

nonn

Also the number of non-isomorphic pairs of set partitions of {1,...,n}.

			Inequivalent representatives of the a(3) = 7 nonnegative integer matrices:
  [3]   [1 2]   [1 1 1]   [1 0]   [0 1]   [1 0 0]   [1 0 0]
                          [0 2]   [1 1]   [0 1 1]   [0 1 0]
                                                    [0 0 1]
Non-isomorphic representatives of the a(3) = 7 pairs of set partitions:
    {{1,2,3}}     {{1,2,3}}
    {{1,2,3}}    {{1},{2,3}}
    {{1,2,3}}   {{1},{2},{3}}
   {{1},{2,3}}   {{1},{2,3}}
   {{1},{2,3}}   {{2},{1,3}}
   {{1},{2,3}}  {{1},{2},{3}}
  {{1},{2},{3}} {{1},{2},{3}}

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A000110, A000258, A001247, A007716, A008277, A049311, A059849, A060639, A116540, A181939, A316983, A318393.

a(n) = (A007716(n) + A316983(n))/2. - Andrew Howroyd, Sep 03 2018

a(6)-a(25) from Andrew Howroyd, Sep 03 2018

Terms a(26) and beyond from Andrew Howroyd, Mar 29 2020

A256035 Number of idempotent basis elements in partition monoid P_n.

Original entry on oeis.org

1, 1, 6, 59, 807, 14102, 301039, 7618613, 223586932, 7482796089, 281882090283

Offset: 0

N. J. A. Sloane, Mar 14 2015

I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014. See Table 3.

Cf. A060639, A256033, A256034, A225797.

cp's OEIS Frontend

A318395 Number of nonnegative integer matrices with values summing to n, up to transposition and permutation of rows and columns.

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