A320797 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons.

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.

Links

Table of n, a(n) for n=0..10.

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]

Crossrefs

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

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

Sequence in context: A369116 A165921 A030136 * A330468 A336450 A372823

Adjacent sequences: A320794 A320795 A320796 * A320798 A320799 A320800

Keyword

nonn,more

Author

Gus Wiseman, Nov 02 2018

Status

approved