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 A324767 Number of recursively anti-transitive rooted identity trees with n nodes. 5
 1, 1, 1, 1, 2, 3, 5, 9, 17, 33, 63, 126, 254, 511, 1039, 2124, 4371, 9059, 18839, 39339, 82385, 173111, 364829, 771010, 1633313 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS An unlabeled rooted tree is recursively anti-transitive if no branch of a branch of any terminal subtree is a branch of the same subtree. It is an identity tree if there are no repeated branches directly under a common root. Also the number of finitary sets with n brackets where, at any level, no element of an element of a set is an element of the same set. For example, the a(8) = 9 finitary sets are (o = {}):   {{{{{{{o}}}}}}}   {{{{o,{{o}}}}}}   {{{o,{{{o}}}}}}   {{o,{{{{o}}}}}}   {{{o},{{{o}}}}}   {o,{{{{{o}}}}}}   {o,{{o,{{o}}}}}   {{o},{{{{o}}}}}   {{o},{o,{{o}}}} The Matula-Goebel numbers of these trees are given by A324766. LINKS EXAMPLE The a(4) = 1 through a(8) = 9 recursively 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(((((o))))))                                                   (((((((o))))))) MATHEMATICA iallt[n_]:=Select[Union[Sort/@Join@@(Tuples[iallt/@#]&/@IntegerPartitions[n-1])], UnsameQ@@#&&Intersection[Union@@#, #]=={}&]; Table[Length[iallt[n]], {n, 10}] CROSSREFS Cf. A000081, A004111, A276625, A279861, A290689, A290760, A304360, A306844, A316500. Cf. A324695, A324751, A324758, A324764 (non-recursive version), A324765 (non-identity version), A324766, A324770, A324839, A324840, A324844. Sequence in context: A080889 A049858 A092483 * A005257 A091697 A109740 Adjacent sequences:  A324764 A324765 A324766 * A324768 A324769 A324770 KEYWORD nonn,more AUTHOR Gus Wiseman, Mar 17 2019 STATUS approved

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Last modified June 24 17:50 EDT 2019. Contains 324330 sequences. (Running on oeis4.)