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

1, 1, 4, 5, 12, 9, 30, 17, 52, 44, 94, 58, 211, 103, 302, 242, 552, 299, 1024, 492, 1592, 1007, 2523, 1257, 4636, 2000, 6661, 3705, 10823, 4567, 18147, 6844, 26606, 12272, 40766, 15056, 67060, 21639, 95884, 37357, 146781, 44585, 230098, 63263, 330889, 106619, 491182, 124756

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.

Links

Table of n, a(n) for n=0..47.

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 A380934 A080277

Adjacent sequences: A330220 A330221 A330222 * A330224 A330225 A330226

Keyword

nonn,hard

Author

Gus Wiseman, Dec 07 2019

Extensions

a(10)-a(11) and a(13) from Erich Friedman, Nov 20 2024

a(12) from Bert Dobbelaere, Apr 29 2025

More terms from Bert Dobbelaere, May 02 2025

Status

approved