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

0,3

Comments

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

Links

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

Formula

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

Example

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}}

Crossrefs

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

Sequence in context: A368773 A192068 A368098 * A151267 A319558 A307251

Adjacent sequences: A318392 A318393 A318394 * A318396 A318397 A318398

Keyword

nonn

Author

Gus Wiseman, Aug 25 2018

Extensions

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

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

Status

approved