cp's OEIS Frontend

A324839 Number of unlabeled rooted identity trees with n nodes where the branches of no branch of the root form a subset of the branches of the root.

%I A324839 #4 Mar 19 2019 07:14:41
%S A324839 1,0,1,1,2,3,8,16,35,74,166,367,831,1878,4299,9857,22775,52777,122957,
%T A324839 287337
%N A324839 Number of unlabeled rooted identity trees with n nodes where the branches of no branch of the root form a subset of the branches of the root.
%C A324839 An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root.
%C A324839 Also the number of finitary sets with n brackets where no element is also a subset. For example, the a(7) = 8 sets are (o = {}):
%C A324839   {{{{{{o}}}}}}
%C A324839   {{{{o,{o}}}}}
%C A324839   {{{o,{{o}}}}}
%C A324839   {{o,{{{o}}}}}
%C A324839   {{o,{o,{o}}}}
%C A324839   {{{o},{{o}}}}
%C A324839   {{o},{{{o}}}}
%C A324839   {{o},{o,{o}}}
%e A324839 The a(1) = 1 through a(8) = 16 rooted identity trees:
%e A324839   o  ((o))  (((o)))  ((o(o)))   (((o(o))))   ((o)(o(o)))    (((o))(o(o)))
%e A324839                      ((((o))))  ((o((o))))   ((o(o(o))))    (((o)(o(o))))
%e A324839                                 (((((o)))))  ((((o(o)))))   (((o(o(o)))))
%e A324839                                              (((o)((o))))   ((o)((o(o))))
%e A324839                                              (((o((o)))))   ((o)(o((o))))
%e A324839                                              ((o)(((o))))   ((o((o(o)))))
%e A324839                                              ((o(((o)))))   ((o(o)((o))))
%e A324839                                              ((((((o))))))  ((o(o((o)))))
%e A324839                                                             (((((o(o))))))
%e A324839                                                             ((((o)((o)))))
%e A324839                                                             ((((o((o))))))
%e A324839                                                             (((o)(((o)))))
%e A324839                                                             (((o(((o))))))
%e A324839                                                             ((o)((((o)))))
%e A324839                                                             ((o((((o))))))
%e A324839                                                             (((((((o)))))))
%t A324839 idall[n_]:=If[n==1,{{}},Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])],UnsameQ@@#&]];
%t A324839 Table[Length[Select[idall[n],And@@Table[!SubsetQ[#,b],{b,#}]&]],{n,10}]
%Y A324839 Cf. A000081, A290760, A304360, A306844, A317787.
%Y A324839 Cf. A324694, A324696, A324704, A324738, A324744, A324758, A324759, A324767, A324770, A324771, A324838, A324840, A324844, A324846.
%K A324839 nonn,more
%O A324839 1,5
%A A324839 _Gus Wiseman_, Mar 18 2019