A318395 - OEIS

%I #14 Mar 29 2020 19:35:39

%S 1,1,3,7,21,54,167,491,1586,5132,17442,60399,216172,790436,2965333,

%T 11365813,44536775,178107679,726716229,3022464373,12807206008,

%U 55253891494,242585471236,1083255591604,4917631017573,22685090928596,106291554085987,505653658171936,2441383079595849

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

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

%H Andrew Howroyd, <a href="/A318395/b318395.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = (A007716(n) + A316983(n))/2. - _Andrew Howroyd_, Sep 03 2018

%e Inequivalent representatives of the a(3) = 7 nonnegative integer matrices:

%e   [3]   [1 2]   [1 1 1]   [1 0]   [0 1]   [1 0 0]   [1 0 0]

%e                           [0 2]   [1 1]   [0 1 1]   [0 1 0]

%e                                                     [0 0 1]

%e Non-isomorphic representatives of the a(3) = 7 pairs of set partitions:

%e     {{1,2,3}}     {{1,2,3}}

%e     {{1,2,3}}    {{1},{2,3}}

%e     {{1,2,3}}   {{1},{2},{3}}

%e    {{1},{2,3}}   {{1},{2,3}}

%e    {{1},{2,3}}   {{2},{1,3}}

%e    {{1},{2,3}}  {{1},{2},{3}}

%e   {{1},{2},{3}} {{1},{2},{3}}

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

%K nonn

%O 0,3

%A _Gus Wiseman_, Aug 25 2018

%E a(6)-a(25) from _Andrew Howroyd_, Sep 03 2018

%E Terms a(26) and beyond from _Andrew Howroyd_, Mar 29 2020