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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321411 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons, with aperiodic parts whose sizes are relatively prime. 5
1, 0, 0, 0, 0, 1, 0, 4, 6, 16, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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 relatively prime row sums (or column sums) and 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(9) = 16 multiset partitions:

  {{12}{122}}  {{112}{1222}}    {{112}{12222}}    {{1112}{11222}}

               {{12}{12222}}    {{122}{11222}}    {{1112}{12222}}

               {{12}{13}{233}}  {{12}{123}{233}}  {{12}{1222222}}

               {{13}{23}{123}}  {{13}{112}{233}}  {{12}{123}{2333}}

                                {{13}{122}{233}}  {{12}{13}{23333}}

                                {{23}{123}{123}}  {{12}{223}{1233}}

                                                  {{13}{112}{2333}}

                                                  {{13}{223}{1233}}

                                                  {{13}{23}{12333}}

                                                  {{23}{122}{1233}}

                                                  {{23}{123}{1233}}

                                                  {{12}{12}{34}{234}}

                                                  {{12}{12}{34}{344}}

                                                  {{12}{13}{14}{234}}

                                                  {{12}{13}{24}{344}}

                                                  {{12}{14}{34}{234}}

CROSSREFS

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

Cf. A320796, A320797, A320803, A320806, A320809, A320813, A321283, A321408-A321413.

Sequence in context: A025618 A133572 A121852 * A242251 A122537 A059736

Adjacent sequences:  A321408 A321409 A321410 * A321412 A321413 A321414

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 April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)