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A297791 Number of series-reduced leaf-balanced rooted trees with n nodes. Number of orderless same-trees with n nodes and all leaves equal to 1. 7
1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 5, 1, 3, 3, 4, 3, 5, 3, 6, 4, 6, 3, 12, 3, 10, 7, 9, 6, 12, 9, 13, 16, 14, 22, 22, 24, 21, 24, 28, 14, 32, 15, 42, 20, 60, 27, 84, 44, 100, 59, 113, 74, 116, 85, 110, 97, 96, 113, 106, 149, 147, 234, 235, 377, 380, 580, 576, 838 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

An unlabeled rooted tree is leaf-balanced if all branches from the same root have the same number of leaves. It is series-reduced if all positive out-degrees are greater than one.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..84

EXAMPLE

The a(13) = 5 trees: (((oo)(oo))(oooo)), ((ooooo)(ooooo)), ((ooo)(ooo)(ooo)), ((oo)(oo)(oo)(oo)), (oooooooooooo).

MATHEMATICA

alltim[n_]:=alltim[n]=If[n===1, {{}}, Join@@Function[c, Select[Union[Sort/@Tuples[alltim/@c]], And[SameQ@@(Count[#, {}, {0, Infinity}]&/@#), FreeQ[#, {_}]]&]]/@IntegerPartitions[n-1]];

Table[Length[alltim[n]], {n, 20}]

CROSSREFS

Cf. A000081, A001190, A001678, A006241, A032305, A289078, A289079, A291441, A291443.

Sequence in context: A233390 A324114 A011776 * A098965 A290087 A016443

Adjacent sequences:  A297788 A297789 A297790 * A297792 A297793 A297794

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 06 2018

EXTENSIONS

a(51) onward from Robert G. Wilson v, Jan 07 2018

STATUS

approved

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Last modified March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)