The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326211 Number of unsortable normal multiset partitions of weight n. 18
 0, 0, 0, 1, 17, 170, 1455, 11678, 92871, 752473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A multiset partition is normal if it covers an initial interval of positive integers. It is unsortable if no permutation has an ordered concatenation, or equivalently if the concatenation of its lexicographically-ordered parts is not weakly increasing. For example, the multiset partition {{1,2},{1,1,1},{2,2,2}} is sortable because the permutation ((1,1,1),(1,2),(2,2,2)) has concatenation (1,1,1,1,2,2,2,2), which is weakly increasing. LINKS FORMULA A255906(n) = a(n) + A326212(n). EXAMPLE The a(3) = 1 and a(4) = 17 multiset partitions: {{1,3},{2}} {{1,1,3},{2}} {{1,2},{1,2}} {{1,2},{1,3}} {{1,2,3},{2}} {{1,2,4},{3}} {{1,3},{2,2}} {{1,3},{2,3}} {{1,3},{2,4}} {{1,3,3},{2}} {{1,3,4},{2}} {{1,4},{2,3}} {{1},{1,3},{2}} {{1},{2,4},{3}} {{1,3},{2},{2}} {{1,3},{2},{3}} {{1,3},{2},{4}} {{1,4},{2},{3}} MATHEMATICA lexsort[f_, c_]:=OrderedQ[PadRight[{f, c}]]; allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]]; sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; Table[Length[Select[Sort[#, lexsort]&/@Join@@mps/@allnorm[n], !OrderedQ[Join@@#]&]], {n, 0, 5}] CROSSREFS Unsortable set partitions are A058681. Sortable normal multiset partitions are A326212. Non-crossing normal multiset partitions are A324171. MM-numbers of unsortable multiset partitions are A326258. Cf. A000108, A016098, A255906, A324170. Cf. A326209, A326210, A326243, A326250, A326255, A326256. Sequence in context: A282922 A023015 A022645 * A164747 A166579 A142169 Adjacent sequences: A326208 A326209 A326210 * A326212 A326213 A326214 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 19 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 4 22:05 EST 2023. Contains 360082 sequences. (Running on oeis4.)