login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319766 Number of non-isomorphic strict intersecting multiset partitions (sets of multisets) of weight n whose dual is also a strict intersecting multiset partition. 6
1, 1, 1, 4, 6, 14, 31, 64, 145, 324, 753 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.

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(5) = 14 multiset partitions:

1: {{1}}

2: {{1,1}}

3: {{1,1,1}}

   {{1,2,2}}

   {{1},{1,1}}

   {{2},{1,2}}

4: {{1,1,1,1}}

   {{1,2,2,2}}

   {{1},{1,1,1}}

   {{1},{1,2,2}}

   {{2},{1,2,2}}

   {{1,2},{2,2}}

5: {{1,1,1,1,1}}

   {{1,1,2,2,2}}

   {{1,2,2,2,2}}

   {{1},{1,1,1,1}}

   {{1},{1,2,2,2}}

   {{2},{1,1,2,2}}

   {{2},{1,2,2,2}}

   {{2},{1,2,3,3}}

   {{1,1},{1,1,1}}

   {{1,1},{1,2,2}}

   {{1,2},{1,2,2}}

   {{1,2},{2,2,2}}

   {{2,2},{1,2,2}}

   {{2},{1,2},{2,2}}

CROSSREFS

Cf. A007716, A281116, A283877, A305854, A306006,  A316980, A316983, A317757, A319616.

Cf. A319752, A319765, A319767, A319768, A319769, A319773, A319774.

Sequence in context: A005202 A342602 A106526 * A108516 A219774 A274208

Adjacent sequences:  A319763 A319764 A319765 * A319767 A319768 A319769

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 27 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 18:30 EDT 2022. Contains 356229 sequences. (Running on oeis4.)