This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A321404 Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons. 4
 1, 0, 0, 0, 1, 0, 1, 1, 3, 4, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Also the number of 0-1 symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, in which no row sums 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 EXAMPLE Non-isomorphic representatives of the a(4) = 1 through a(10) = 6 set multipartitions:    4: {{1,2},{1,2}}    6: {{1,2},{1,3},{2,3}}    7: {{1,3},{2,3},{1,2,3}}    8: {{2,3},{1,2,3},{1,2,3}}    8: {{1,2},{1,2},{3,4},{3,4}}    8: {{1,2},{1,3},{2,4},{3,4}}    9: {{1,2,3},{1,2,3},{1,2,3}}    9: {{1,2},{1,2},{3,4},{2,3,4}}    9: {{1,2},{1,3},{1,4},{2,3,4}}    9: {{1,2},{1,4},{3,4},{2,3,4}}   10: {{1,2},{1,2},{1,3,4},{2,3,4}}   10: {{1,2},{2,4},{1,3,4},{2,3,4}}   10: {{1,3},{2,4},{1,3,4},{2,3,4}}   10: {{1,4},{2,4},{3,4},{1,2,3,4}}   10: {{1,2},{1,2},{3,4},{3,5},{4,5}}   10: {{1,2},{1,3},{2,4},{3,5},{4,5}} CROSSREFS Cf. A007716, A049311, A135588, A138178, A283877, A302545, A316983. Cf. A320797, A320798, A320811, A320812, A321403, A321404, A321405, A321406. Sequence in context: A085841 A163483 A004784 * A024687 A072631 A085196 Adjacent sequences:  A321401 A321402 A321403 * A321405 A321406 A321407 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 15 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.

Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)