cp's OEIS Frontend

A326211 Number of unsortable normal multiset partitions of weight n.

%I A326211 #8 Jun 21 2019 22:44:20
%S A326211 0,0,0,1,17,170,1455,11678,92871,752473
%N A326211 Number of unsortable normal multiset partitions of weight n.
%C A326211 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.
%F A326211 A255906(n) = a(n) + A326212(n).
%e A326211 The a(3) = 1 and a(4) = 17 multiset partitions:
%e A326211   {{1,3},{2}}  {{1,1,3},{2}}
%e A326211                {{1,2},{1,2}}
%e A326211                {{1,2},{1,3}}
%e A326211                {{1,2,3},{2}}
%e A326211                {{1,2,4},{3}}
%e A326211                {{1,3},{2,2}}
%e A326211                {{1,3},{2,3}}
%e A326211                {{1,3},{2,4}}
%e A326211                {{1,3,3},{2}}
%e A326211                {{1,3,4},{2}}
%e A326211                {{1,4},{2,3}}
%e A326211                {{1},{1,3},{2}}
%e A326211                {{1},{2,4},{3}}
%e A326211                {{1,3},{2},{2}}
%e A326211                {{1,3},{2},{3}}
%e A326211                {{1,3},{2},{4}}
%e A326211                {{1,4},{2},{3}}
%t A326211 lexsort[f_,c_]:=OrderedQ[PadRight[{f,c}]];
%t A326211 allnorm[n_]:=If[n<=0,{{}},Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1]];
%t A326211 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A326211 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A326211 Table[Length[Select[Sort[#,lexsort]&/@Join@@mps/@allnorm[n],!OrderedQ[Join@@#]&]],{n,0,5}]
%Y A326211 Unsortable set partitions are A058681.
%Y A326211 Sortable normal multiset partitions are A326212.
%Y A326211 Non-crossing normal multiset partitions are A324171.
%Y A326211 MM-numbers of unsortable multiset partitions are A326258.
%Y A326211 Cf. A000108, A016098, A255906, A324170.
%Y A326211 Cf. A326209, A326210, A326243, A326250, A326255, A326256.
%K A326211 nonn,more
%O A326211 0,5
%A A326211 _Gus Wiseman_, Jun 19 2019