A330223 Number of non-isomorphic achiral multiset partitions of weight n.

1, 1, 4, 5, 12, 9, 30, 17, 52, 44, 94, 58

Offset

0,3

Comments

A multiset partition is a finite multiset of finite nonempty multisets. It is achiral if it is not changed by any permutation of the vertices.

a(13) = 103. - Erich Friedman, Nov 20 2024

Links

Table of n, a(n) for n=0..11.

Example

Non-isomorphic representatives of the a(1) = 1 through a(5) = 9 multiset partitions:
  {1}  {11}    {111}      {1111}        {11111}
       {12}    {123}      {1122}        {12345}
       {1}{1}  {1}{11}    {1234}        {1}{1111}
       {1}{2}  {1}{1}{1}  {1}{111}      {11}{111}
               {1}{2}{3}  {11}{11}      {1}{1}{111}
                          {11}{22}      {1}{11}{11}
                          {12}{12}      {1}{1}{1}{11}
                          {1}{1}{11}    {1}{1}{1}{1}{1}
                          {1}{2}{12}    {1}{2}{3}{4}{5}
                          {1}{1}{1}{1}
                          {1}{1}{2}{2}
                          {1}{2}{3}{4}
Non-isomorphic representatives of the a(6) = 30 multiset partitions:
  {111111}  {1}{11111}  {1}{1}{1111}  {1}{1}{1}{111}  {1}{1}{1}{1}{11}
  {111222}  {11}{1111}  {1}{11}{111}  {1}{1}{11}{11}  {1}{1}{2}{2}{12}
  {112233}  {111}{111}  {11}{11}{11}  {1}{2}{11}{22}
  {123456}  {111}{222}  {11}{12}{22}  {1}{2}{12}{12}
            {112}{122}  {11}{22}{33}  {1}{2}{3}{123}    {1}{1}{1}{1}{1}{1}
            {12}{1122}  {1}{2}{1122}                    {1}{1}{1}{2}{2}{2}
            {123}{123}  {12}{12}{12}                    {1}{1}{2}{2}{3}{3}
                        {12}{13}{23}                    {1}{2}{3}{4}{5}{6}

Crossrefs

Planted achiral trees are A003238.

Achiral set-systems are counted by A083323.

BII-numbers of achiral set-systems are A330217.

Achiral integer partitions are counted by A330224.

Non-isomorphic fully chiral multiset partitions are A330227.

MM-numbers of achiral multisets of multisets are A330232.

Achiral factorizations are A330234.

Cf. A001055, A007716, A283877, A317533, A330098, A330233.

Sequence in context: A344372 A034773 A323766 * A325688 A080277 A047608

Adjacent sequences: A330220 A330221 A330222 * A330224 A330225 A330226

Keyword

nonn,more,hard

Author

Gus Wiseman, Dec 07 2019

Extensions

a(10)-a(11) from Erich Friedman, Nov 20 2024

Status

approved