cp's OEIS Frontend

A332872 Number of ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.

%I A332872 #5 Mar 06 2020 22:39:56
%S A332872 1,1,3,10,34,116,396,1352,4616,15760
%N A332872 Number of ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.
%C A332872 After initial terms, first differs from A291292 at a(7) = 1352, A291292(8) = 1353.
%C A332872 Conjectured to be the same as A007052, shifted right once.
%e A332872 The a(1) = 1 through a(3) = 10 ordered set partitions:
%e A332872   {{1}}  {{1,2}}    {{1,2,3}}
%e A332872          {{1},{2}}  {{1},{2,3}}
%e A332872          {{2},{1}}  {{1,2},{3}}
%e A332872                     {{1,3},{2}}
%e A332872                     {{2},{1,3}}
%e A332872                     {{2,3},{1}}
%e A332872                     {{3},{1,2}}
%e A332872                     {{1},{2},{3}}
%e A332872                     {{1},{3},{2}}
%e A332872                     {{2},{1},{3}}
%t A332872 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A332872 Table[Length[Select[Join@@Permutations/@sps[Range[n]],!MatchQ[#,{___,{___,a_,___},__,{___,b_,___},___}/;a>b]&]],{n,0,5}]
%Y A332872 Row sums of A332673.
%Y A332872 Set partitions are A000110.
%Y A332872 Ordered set-partitions are A000670.
%Y A332872 Unimodal sequences covering an initial interval are A007052.
%Y A332872 Cf. A001523, A056242, A097805, A328509, A332280, A332283, A332294, A332724.
%K A332872 nonn,more
%O A332872 0,3
%A A332872 _Gus Wiseman_, Mar 06 2020