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

1,5

Comments

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

Links

Table of n, a(n) for n=1..15.

Example

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))))

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}]

Crossrefs

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

Sequence in context: A265257 A005294 A052943 * A184307 A032580 A002014

Adjacent sequences: A325694 A325695 A325696 * A325698 A325699 A325700

Keyword

nonn,more

Author

Gus Wiseman, May 17 2019

Status

approved