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A330058 Number of non-isomorphic multiset partitions of weight n with at least one endpoint. 8
0, 1, 2, 7, 21, 68, 214, 706, 2335, 7968, 27661 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

An endpoint is a vertex appearing only once (degree 1).

Also the number of non-isomorphic multiset partitions of weight n with at least one singleton.

LINKS

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

Wikipedia, Degree (graph theory)

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions:

  {1}  {12}    {122}      {1222}

       {1}{2}  {123}      {1233}

               {1}{22}    {1234}

               {1}{23}    {1}{222}

               {2}{12}    {12}{22}

               {1}{2}{2}  {1}{233}

               {1}{2}{3}  {12}{33}

                          {1}{234}

                          {12}{34}

                          {13}{23}

                          {2}{122}

                          {3}{123}

                          {1}{1}{23}

                          {1}{2}{22}

                          {1}{2}{33}

                          {1}{2}{34}

                          {1}{3}{23}

                          {2}{2}{12}

                          {1}{2}{2}{2}

                          {1}{2}{3}{3}

                          {1}{2}{3}{4}

CROSSREFS

The case of set-systems is A330053 (singletons) or A330052 (endpoints).

The complement is counted by A302545.

Cf. A007716, A283877, A306005, A330054, A330055, A330059.

Sequence in context: A126133 A186240 A274203 * A220726 A127540 A319852

Adjacent sequences:  A330055 A330056 A330057 * A330059 A330060 A330061

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 30 2019

STATUS

approved

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Last modified March 28 17:51 EDT 2020. Contains 333103 sequences. (Running on oeis4.)