A324971 - OEIS

%I #6 Mar 22 2019 00:33:48

%S 0,0,0,0,0,1,4,12,31,79,192,459,1082,2537,5922,13816,32222,75254,

%T 176034,412667,969531,2283278

%N Number of rooted identity trees with n vertices whose non-leaf terminal subtrees are not all different.

%C A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root.

%e The a(6) = 1 through a(8) = 12 trees:

%e   ((o)((o)))  ((o)(o(o)))   (o(o)(o(o)))

%e               (o(o)((o)))   (((o))(o(o)))

%e               (((o)((o))))  (((o)(o(o))))

%e               ((o)(((o))))  ((o)((o(o))))

%e                             ((o)(o((o))))

%e                             ((o(o)((o))))

%e                             (o((o)((o))))

%e                             (o(o)(((o))))

%e                             ((((o)((o)))))

%e                             (((o))(((o))))

%e                             (((o)(((o)))))

%e                             ((o)((((o)))))

%t rits[n_]:=Join@@Table[Select[Union[Sort/@Tuples[rits/@ptn]],UnsameQ@@#&],{ptn,IntegerPartitions[n-1]}];

%t Table[Length[Select[rits[n],!UnsameQ@@Cases[#,{__},{0,Infinity}]&]],{n,10}]

%Y The Matula-Goebel numbers of these trees are given by A324970.

%Y Cf. A000081, A004111, A290689, A317713, A324850, A324922, A324923, A324924, A324931, A324935, A324936, A324979.

%K nonn,more

%O 1,7

%A _Gus Wiseman_, Mar 21 2019