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A320804 Number of non-isomorphic multiset partitions of weight n with no singletons in which all parts are aperiodic multisets. 5
1, 0, 1, 2, 6, 13, 41, 104, 326, 958, 3096 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also the number of nonnegative integer matrices with (1) sum of elements equal to n, (2) no zero columns, (3) no rows summing to 0 or 1, and (4) no rows whose nonzero entries have a common divisor > 1, up to row and column permutations.

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(2) = 1 through a(5) = 13 multiset partitions with aperiodic parts and no singletons:

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

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

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

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

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

                      {{1,3},{2,3}}  {{1,2,3,4,5}}

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

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

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

                                     {{1,2},{3,4,5}}

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

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

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

CROSSREFS

Cf. A000740, A000837, A007716, A007916, A100953, A301700, A302545, A303386, A303546, A303707, A303708, A320797-A320813.

Sequence in context: A052450 A231385 A001373 * A284223 A241784 A211995

Adjacent sequences:  A320801 A320802 A320803 * A320805 A320806 A320807

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 06 2018

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)