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A331578 Number of labeled series-reduced rooted trees with n vertices and more than two branches of the root. 6
0, 0, 0, 4, 5, 186, 847, 17928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A rooted tree is series-reduced if no vertex (including the root) has degree 2.

Also labeled lone-child-avoiding rooted trees with n vertices and more than two branches, where a rooted tree is lone-child-avoiding if no vertex has exactly one child.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

Non-isomorphic representatives of the a(7) = 847 trees (in the format root[branches]) are:

  1[2,3,4[5,6,7]]

  1[2,3,4,5[6,7]]

  1[2,3,4,5,6,7]

MATHEMATICA

lrt[set_]:=If[Length[set]==0, {}, Join@@Table[Apply[root, #]&/@Join@@Table[Tuples[lrt/@stn], {stn, sps[DeleteCases[set, root]]}], {root, set}]];

Table[Length[Select[lrt[Range[n]], Length[#]>2&&FreeQ[#, _[_]]&]], {n, 6}]

CROSSREFS

The non-series-reduced version is A331577.

The unlabeled version is A331488.

Lone-child-avoiding rooted trees are counted by A001678.

Topologically series-reduced rooted trees are counted by A001679.

Labeled topologically series-reduced rooted trees are counted by A060313.

Labeled lone-child-avoiding rooted trees are counted by A060356.

Matula-Goebel numbers of lone-child-avoiding rooted trees are A291636.

Matula-Goebel numbers of series-reduced rooted trees are A331489.

Cf. A000014, A000169, A000669, A005512, A108919, A206429, A331233, A331490.

Sequence in context: A270551 A041409 A101076 * A041745 A298224 A051152

Adjacent sequences:  A331575 A331576 A331577 * A331579 A331580 A331581

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 21 2020

STATUS

approved

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Last modified September 29 10:54 EDT 2020. Contains 337428 sequences. (Running on oeis4.)