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A320803 Number of non-isomorphic multiset partitions of weight n in which all parts are aperiodic multisets. 4
1, 1, 3, 7, 21, 56, 174, 517, 1664, 5383, 18199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A multiset is aperiodic if its multiplicities are relatively prime.

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

LINKS

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

EXAMPLE

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                                   {{1},{1},{1},{1}}

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

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

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

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

CROSSREFS

Cf. A000740, A000837, A007716, A007916, A100953, A301700, A303386, A303546, A303707, A303708, A303709, A303710, A320800-A320810.

Sequence in context: A151267 A319558 A307251 * A262184 A091489 A047087

Adjacent sequences:  A320800 A320801 A320802 * A320804 A320805 A320806

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 06 2018

STATUS

approved

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)