

A321412


Number of nonisomorphic selfdual multiset partitions of weight n with no singletons and with aperiodic parts.


1



1, 0, 0, 0, 1, 1, 3, 4, 12, 20, 42
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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

Nonisomorphic 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



