A320797 - OEIS

A320797

Number of non-isomorphic self-dual multiset partitions of weight n with no singletons.

%I #7 Nov 05 2018 21:01:08

%S 1,0,1,1,3,4,9,15,33,60,121

%N Number of non-isomorphic self-dual multiset partitions of weight n with no singletons.

%C Also the number of nonnegative integer square symmetric matrices with sum of elements equal to n and no rows or columns summing to 0 or 1, up to row and column permutations.

%e Non-isomorphic representatives of the a(2) = 1 through a(7) = 15 multiset partitions:

%e {{11}} {{111}} {{1111}} {{11111}} {{111111}} {{1111111}}

%e {{11}{22}} {{11}{122}} {{111}{222}} {{111}{1222}}

%e {{12}{12}} {{11}{222}} {{112}{122}} {{111}{2222}}

%e {{12}{122}} {{11}{2222}} {{112}{1222}}

%e {{12}{1222}} {{11}{22222}}

%e {{22}{1122}} {{12}{12222}}

%e {{11}{22}{33}} {{122}{1122}}

%e {{11}{23}{23}} {{22}{11222}}

%e {{12}{13}{23}} {{11}{12}{233}}

%e {{11}{22}{233}}

%e {{11}{22}{333}}

%e {{11}{23}{233}}

%e {{12}{12}{333}}

%e {{12}{13}{233}}

%e {{13}{23}{123}}

%e Inequivalent representatives of the a(6) = 9 symmetric matrices with no rows or columns summing to 1:

%e [6]

%e .

%e [3 0] [2 1] [4 0] [3 1] [2 2]

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

%e .

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

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

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

%Y Cf. A000219, A007716, A302545, A316980, A316983, A319560, A319616, A319721.

%Y Cf. A320796, A320798, A320799, A320804, A320811, A320812, A320813.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Nov 02 2018