

A331488


Number of unlabeled lonechildavoiding rooted trees with n vertices and more than two branches (of the root).


9



0, 0, 0, 1, 1, 2, 3, 6, 10, 20, 36, 70, 134, 263, 513, 1022, 2030, 4076, 8203, 16614, 33738, 68833, 140796, 288989, 594621, 1226781, 2536532, 5256303, 10913196, 22700682, 47299699, 98714362, 206323140, 431847121, 905074333, 1899247187, 3990145833, 8392281473
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OFFSET

1,6


COMMENTS

Also the number of lonechildavoiding rooted trees with n vertices and more than two branches.


LINKS

Table of n, a(n) for n=1..38.
David Callan, A signreversing involution to count labeled lonechildavoiding trees, arXiv:1406.7784 [math.CO], (30June2014)
Eric Weisstein's World of Mathematics, Seriesreduced tree.
Gus Wiseman, Sequences counting seriesreduced and lonechildavoiding trees by number of vertices.


FORMULA

For n > 1, a(n) = A001679(n)  A001678(n).


EXAMPLE

The a(4) = 1 through a(9) = 10 trees:
(ooo) (oooo) (ooooo) (oooooo) (ooooooo) (oooooooo)
(oo(oo)) (oo(ooo)) (oo(oooo)) (oo(ooooo))
(ooo(oo)) (ooo(ooo)) (ooo(oooo))
(oooo(oo)) (oooo(ooo))
(o(oo)(oo)) (ooooo(oo))
(oo(o(oo))) (o(oo)(ooo))
(oo(o(ooo)))
(oo(oo)(oo))
(oo(oo(oo)))
(ooo(o(oo)))


MATHEMATICA

urt[n_]:=Join@@Table[Union[Sort/@Tuples[urt/@ptn]], {ptn, IntegerPartitions[n1]}];
Table[Length[Select[urt[n], Length[#]>2&&FreeQ[#, {_}]&]], {n, 10}]


CROSSREFS

The not necessarily lonechildavoiding version is A331233.
The MatulaGoebel numbers of these trees are listed by A331490.
A000081 counts unlabeled rooted trees.
A001678 counts lonechildavoiding rooted trees.
A001679 counts topologically seriesreduced rooted trees.
A291636 lists MatulaGoebel numbers of lonechildavoiding rooted trees.
A331489 lists MatulaGoebel numbers of seriesreduced rooted trees.
Cf. A000014, A000669, A004250, A007097, A007821, A033942, A060313, A060356, A061775, A109082, A109129, A196050, A276625, A330943.
Sequence in context: A047131 A231331 A008927 * A052525 A006606 A120421
Adjacent sequences: A331485 A331486 A331487 * A331489 A331490 A331491


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jan 20 2020


EXTENSIONS

a(37)a(38) from Jinyuan Wang, Jun 26 2020
Terminology corrected (lonechildavoiding, not seriesreduced) by Gus Wiseman, May 10 2021


STATUS

approved



