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

Author

Gus Wiseman, Aug 25 2018

Keywords

• nonn

Comments

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

Examples

			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}}
		

Links

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

Crossrefs

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

Formula

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

Extensions

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

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