A324936 Number of unlabeled rooted trees with n vertices whose non-leaf terminal subtrees are all different.

1, 1, 2, 4, 8, 17, 37, 83, 189, 436, 1014, 2373, 5578, 13156, 31104, 73665, 174665, 414427, 983606, 2334488

Offset

1,3

Comments

The Matula-Goebel numbers of these trees are given by A324935.

Links

Table of n, a(n) for n=1..20.

Example

The a(1) = 1 through a(6) = 17 trees:
  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)
          ((o))  ((oo))   ((ooo))    ((oooo))
                 (o(o))   (o(oo))    (o(ooo))
                 (((o)))  (oo(o))    (oo(oo))
                          (((oo)))   (ooo(o))
                          ((o(o)))   (((ooo)))
                          (o((o)))   ((o)(oo))
                          ((((o))))  ((o(oo)))
                                     ((oo(o)))
                                     (o((oo)))
                                     (o(o(o)))
                                     (oo((o)))
                                     ((((oo))))
                                     (((o(o))))
                                     ((o((o))))
                                     (o(((o))))
                                     (((((o)))))

Mathematica

durt[n_]:=Join@@Table[Select[Union[Sort/@Tuples[durt/@ptn]], UnsameQ@@Cases[#, {__}, {0, Infinity}]&], {ptn, IntegerPartitions[n-1]}];
Table[Length[durt[n]], {n, 10}]

Crossrefs

Cf. A000081, A004111, A290689, A317713, A324850, A324922, A324923, A324924, A324931, A324935.

Sequence in context: A004148 A292460 A085022 * A358453 A331783 A003426

Adjacent sequences: A324933 A324934 A324935 * A324937 A324938 A324939

Keyword

nonn,more

Author

Gus Wiseman, Mar 21 2019

Status

approved