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 A324979 Number of rooted trees with n vertices that are not identity trees but whose non-leaf terminal subtrees are all different. 2
 0, 0, 1, 2, 5, 12, 29, 70, 168, 402, 959, 2284, 5434, 12923, 30727, 73055, 173678, 412830 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root. LINKS EXAMPLE The a(3) = 1 through a(6) = 12 trees:   (oo)  (ooo)   (oooo)    (ooooo)         ((oo))  ((ooo))   ((oooo))                 (o(oo))   (o(ooo))                 (oo(o))   (oo(oo))                 (((oo)))  (ooo(o))                           (((ooo)))                           ((o)(oo))                           ((o(oo)))                           ((oo(o)))                           (o((oo)))                           (oo((o)))                           ((((oo)))) MATHEMATICA rits[n_]:=Join@@Table[Union[Sort/@Tuples[rits/@ptn]], {ptn, IntegerPartitions[n-1]}]; Table[Length[Select[rits[n], And[UnsameQ@@Cases[#, {__}, {0, Infinity}], !And@@Cases[mgtree[#], q:{__}:>UnsameQ@@q, {0, Infinity}]]&]], {n, 10}] CROSSREFS The Matula-Goebel numbers of these trees are given by A324978. Cf. A000081, A004111, A290689, A317713, A324850, A324922, A324923, A324924, A324931, A324935, A324936, A324970, A324971. Sequence in context: A067687 A291235 A130009 * A048624 A176981 A215936 Adjacent sequences:  A324976 A324977 A324978 * A324980 A324981 A324982 KEYWORD nonn,more AUTHOR Gus Wiseman, Mar 21 2019 STATUS approved

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Last modified June 16 03:44 EDT 2019. Contains 324145 sequences. (Running on oeis4.)