A324971 Number of rooted identity trees with n vertices whose non-leaf terminal subtrees are not all different.

0, 0, 0, 0, 0, 1, 4, 12, 31, 79, 192, 459, 1082, 2537, 5922, 13816, 32222, 75254, 176034, 412667, 969531, 2283278

Offset

1,7

Comments

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

Links

Table of n, a(n) for n=1..22.

Example

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

Mathematica

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

Crossrefs

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

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

Sequence in context: A190376 A276785 A171844 * A273387 A328240 A369817

Adjacent sequences: A324968 A324969 A324970 * A324972 A324973 A324974

Keyword

nonn,more

Author

Gus Wiseman, Mar 21 2019

Status

approved