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 A324764 Number of anti-transitive rooted identity trees with n nodes. 17
 1, 1, 1, 1, 3, 4, 9, 20, 41, 89, 196, 443, 987, 2246, 5114, 11757, 27122, 62898, 146392, 342204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root. It is anti-transitive if the branches of the branches of the root are disjoint from the branches of the root. Also the number of finitary sets S with n brackets where no element of an element of S is also an element of S. For example, the a(8) = 20 finitary sets are (o = {}):   {{{{{{{o}}}}}}}   {{{{{o,{o}}}}}}   {{{{o,{{o}}}}}}   {{{o,{{{o}}}}}}   {{{o,{o,{o}}}}}   {{{{o},{{o}}}}}   {{o,{{{{o}}}}}}   {{o,{{o,{o}}}}}   {{o,{o,{{o}}}}}   {{{o},{{{o}}}}}   {{{o},{o,{o}}}}   {{o,{o},{{o}}}}   {o,{{{{{o}}}}}}   {o,{{{o,{o}}}}}   {o,{{o,{{o}}}}}   {o,{{o},{{o}}}}   {{o},{{{{o}}}}}   {{o},{{o,{o}}}}   {{o},{o,{{o}}}}   {{{o}},{o,{o}}} LINKS Gus Wiseman, The a(9) = 41 anti-transitive rooted identity trees. EXAMPLE The a(1) = 1 through a(7) = 9 anti-transitive rooted identity trees:   o  (o)  ((o))  (((o)))  ((o(o)))   (((o(o))))   ((o(o(o))))                           (o((o)))   ((o((o))))   (o((o(o))))                           ((((o))))  (o(((o))))   ((((o(o)))))                                      (((((o)))))  (((o)((o))))                                                   (((o((o)))))                                                   ((o)(((o))))                                                   ((o(((o)))))                                                   (o((((o)))))                                                   ((((((o)))))) MATHEMATICA idall[n_]:=If[n==1, {{}}, Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])], UnsameQ@@#&]]; Table[Length[Select[idall[n], Intersection[Union@@#, #]=={}&]], {n, 10}] CROSSREFS Cf. A000081, A004111, A276625, A279861, A290689, A304360, A306844 (non-identity version), A316500, A317787, A318185. Cf. A324694, A324751, A324756, A324758, A324765, A324767, A324768, A324770, A324839, A324840, A324844. Sequence in context: A247579 A282615 A049978 * A092763 A232955 A116868 Adjacent sequences:  A324761 A324762 A324763 * A324765 A324766 A324767 KEYWORD nonn,more AUTHOR Gus Wiseman, Mar 17 2019 STATUS approved

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Last modified June 5 11:44 EDT 2020. Contains 334840 sequences. (Running on oeis4.)