A325697 Number of rooted trees with n vertices with no proper terminal subtree appearing at only one position.

1, 0, 1, 1, 2, 2, 5, 5, 11, 13, 27, 30, 69, 76, 168

Offset: 1

Author

Gus Wiseman, May 17 2019

Keywords

• nonn
• more

Comments

The Matula-Goebel numbers of these trees are given by A325661.

Examples

			The a(4) = 1 through a(9) = 11 rooted trees:
  (ooo)  (oooo)    (ooooo)    (oooooo)      (ooooooo)      (oooooooo)
         ((o)(o))  (o(o)(o))  ((oo)(oo))    (o(oo)(oo))    ((ooo)(ooo))
                              (oo(o)(o))    (ooo(o)(o))    (oo(oo)(oo))
                              ((o)(o)(o))   (o(o)(o)(o))   (oooo(o)(o))
                              (((o))((o)))  (o((o))((o)))  (oo(o)(o)(o))
                                                           (((oo))((oo)))
                                                           ((o)(o)(o)(o))
                                                           ((o(o))(o(o)))
                                                           (oo((o))((o)))
                                                           ((o)((o))((o)))
                                                           ((((o)))(((o))))
		

Crossrefs

Cf. A000081, A001694, A004111, A290689, A306844, A317713, A324936, A324971, A325661.

Programs

Mathematica

urt[n_]:=Join@@Table[Union[Sort/@Tuples[urt/@ptn]],{ptn,IntegerPartitions[n-1]}];
Table[Length[Select[urt[n],!MemberQ[Length/@Split[Sort[Extract[#,Most[Position[#,_List]]]]],1]&]],{n,15}]