cp's OEIS Frontend

A324979 Number of rooted trees with n vertices that are not identity trees but whose non-leaf terminal subtrees are all different.

%I A324979 #4 Mar 22 2019 00:34:02
%S A324979 0,0,1,2,5,12,29,70,168,402,959,2284,5434,12923,30727,73055,173678,
%T A324979 412830
%N A324979 Number of rooted trees with n vertices that are not identity trees but whose non-leaf terminal subtrees are all different.
%C A324979 An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root.
%e A324979 The a(3) = 1 through a(6) = 12 trees:
%e A324979   (oo)  (ooo)   (oooo)    (ooooo)
%e A324979         ((oo))  ((ooo))   ((oooo))
%e A324979                 (o(oo))   (o(ooo))
%e A324979                 (oo(o))   (oo(oo))
%e A324979                 (((oo)))  (ooo(o))
%e A324979                           (((ooo)))
%e A324979                           ((o)(oo))
%e A324979                           ((o(oo)))
%e A324979                           ((oo(o)))
%e A324979                           (o((oo)))
%e A324979                           (oo((o)))
%e A324979                           ((((oo))))
%t A324979 rits[n_]:=Join@@Table[Union[Sort/@Tuples[rits/@ptn]],{ptn,IntegerPartitions[n-1]}];
%t A324979 Table[Length[Select[rits[n],And[UnsameQ@@Cases[#,{__},{0,Infinity}],!And@@Cases[mgtree[#],q:{__}:>UnsameQ@@q,{0,Infinity}]]&]],{n,10}]
%Y A324979 The Matula-Goebel numbers of these trees are given by A324978.
%Y A324979 Cf. A000081, A004111, A290689, A317713, A324850, A324922, A324923, A324924, A324931, A324935, A324936, A324970, A324971.
%K A324979 nonn,more
%O A324979 1,4
%A A324979 _Gus Wiseman_, Mar 21 2019