login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321412 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons and with aperiodic parts. 1
1, 0, 0, 0, 1, 1, 3, 4, 12, 20, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

A multiset is aperiodic if its multiplicities are relatively prime.

Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with no row or column having a common divisor > 1 or summing to 1.

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}}.

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(5) = 1 through a(8) = 12 multiset partitions:

{{12}{12}}  {{12}{122}}  {{112}{122}}    {{112}{1222}}    {{1112}{1222}}

                         {{12}{1222}}    {{12}{12222}}    {{112}{12222}}

                         {{12}{13}{23}}  {{12}{13}{233}}  {{12}{122222}}

                                         {{13}{23}{123}}  {{122}{11222}}

                                                          {{12}{123}{233}}

                                                          {{12}{13}{2333}}

                                                          {{13}{112}{233}}

                                                          {{13}{122}{233}}

                                                          {{13}{23}{1233}}

                                                          {{23}{123}{123}}

                                                          {{12}{12}{34}{34}}

                                                          {{12}{13}{24}{34}}

CROSSREFS

Cf. A000219, A007716, A120733, A138178, A302545, A316983, A319616.

Cf. A320796, A320797, A320803, A320806, A320809, A320813, A321408, A321410, A321411.

Sequence in context: A124817 A306005 A124818 * A124638 A124639 A279696

Adjacent sequences:  A321409 A321410 A321411 * A321413 A321414 A321415

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 16 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 18:35 EST 2021. Contains 349424 sequences. (Running on oeis4.)