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A316766 Number of series-reduced locally stable rooted identity trees whose leaves form an integer partition of n. 0
1, 1, 2, 3, 6, 13, 30, 72, 180, 458, 1194, 3160, 8459, 22881, 62417, 171526, 474405, 1319395, 3687711, 10352696, 29178988 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A rooted tree is series-reduced if every non-leaf node has at least two branches. It is locally stable if no branch is a submultiset of any other branch of the same root. It is an identity tree if no branch appears multiple times under the same root.

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

The a(6) = 13 trees:

6,

(15),

(1(14)),

(1(1(13))),

(1(1(1(12)))),

(1(23)), (2(13)), (3(12)), (123),

(1(2(12))), (2(1(12))), (12(12)),

(24).

Example of non-stable trees are ((12)(123)) and ((12)(12(12))).

MATHEMATICA

submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]];

stableQ[u_]:=Apply[And, Outer[#1==#2||!submultisetQ[#1, #2]&&!submultisetQ[#2, #1]&, u, u, 1], {0, 1}];

nms[n_]:=nms[n]=Prepend[Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]], And[UnsameQ@@#, stableQ[#]]&], {ptn, Rest[IntegerPartitions[n]]}], {n}];

Table[Length[nms[n]], {n, 10}]

CROSSREFS

Cf. A000081, A000669, A001678, A004111, A141268, A292504, A300660, A316467, A316474, A316653, A316654, A316656.

Sequence in context: A174191 A052937 A005554 * A300660 A077212 A076836

Adjacent sequences:  A316763 A316764 A316765 * A316767 A316768 A316769

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 12 2018

EXTENSIONS

a(18)-a(21) from Robert Price, Sep 14 2018

STATUS

approved

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Last modified November 22 03:35 EST 2019. Contains 329386 sequences. (Running on oeis4.)