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A320797
Number of non-isomorphic self-dual multiset partitions of weight n with no singletons.
18
1, 0, 1, 1, 3, 4, 9, 15, 33, 60, 121
OFFSET
0,5
COMMENTS
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.
EXAMPLE
Non-isomorphic representatives of the a(2) = 1 through a(7) = 15 multiset partitions:
{{11}} {{111}} {{1111}} {{11111}} {{111111}} {{1111111}}
{{11}{22}} {{11}{122}} {{111}{222}} {{111}{1222}}
{{12}{12}} {{11}{222}} {{112}{122}} {{111}{2222}}
{{12}{122}} {{11}{2222}} {{112}{1222}}
{{12}{1222}} {{11}{22222}}
{{22}{1122}} {{12}{12222}}
{{11}{22}{33}} {{122}{1122}}
{{11}{23}{23}} {{22}{11222}}
{{12}{13}{23}} {{11}{12}{233}}
{{11}{22}{233}}
{{11}{22}{333}}
{{11}{23}{233}}
{{12}{12}{333}}
{{12}{13}{233}}
{{13}{23}{123}}
Inequivalent representatives of the a(6) = 9 symmetric matrices with no rows or columns summing to 1:
[6]
.
[3 0] [2 1] [4 0] [3 1] [2 2]
[0 3] [1 2] [0 2] [1 1] [2 0]
.
[2 0 0] [2 0 0] [1 1 0]
[0 2 0] [0 1 1] [1 0 1]
[0 0 2] [0 1 1] [0 1 1]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 02 2018
STATUS
approved