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A324979 Number of rooted trees with n vertices that are not identity trees but whose non-leaf terminal subtrees are all different. 2
0, 0, 1, 2, 5, 12, 29, 70, 168, 402, 959, 2284, 5434, 12923, 30727, 73055, 173678, 412830 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root.

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

The a(3) = 1 through a(6) = 12 trees:

  (oo)  (ooo)   (oooo)    (ooooo)

        ((oo))  ((ooo))   ((oooo))

                (o(oo))   (o(ooo))

                (oo(o))   (oo(oo))

                (((oo)))  (ooo(o))

                          (((ooo)))

                          ((o)(oo))

                          ((o(oo)))

                          ((oo(o)))

                          (o((oo)))

                          (oo((o)))

                          ((((oo))))

MATHEMATICA

rits[n_]:=Join@@Table[Union[Sort/@Tuples[rits/@ptn]], {ptn, IntegerPartitions[n-1]}];

Table[Length[Select[rits[n], And[UnsameQ@@Cases[#, {__}, {0, Infinity}], !And@@Cases[mgtree[#], q:{__}:>UnsameQ@@q, {0, Infinity}]]&]], {n, 10}]

CROSSREFS

The Matula-Goebel numbers of these trees are given by A324978.

Cf. A000081, A004111, A290689, A317713, A324850, A324922, A324923, A324924, A324931, A324935, A324936, A324970, A324971.

Sequence in context: A067687 A291235 A130009 * A048624 A176981 A215936

Adjacent sequences:  A324976 A324977 A324978 * A324980 A324981 A324982

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 21 2019

STATUS

approved

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Last modified June 16 03:44 EDT 2019. Contains 324145 sequences. (Running on oeis4.)