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A318689 Number of powerful uniform rooted trees with n nodes. 3
1, 1, 2, 3, 5, 6, 11, 12, 19, 23, 35, 36, 63, 64, 98, 112, 173, 174, 291, 292 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A powerful uniform rooted tree with n nodes is either a single powerful uniform branch with n-1 nodes, or a powerful uniform multiset (all multiplicities are equal to the same number > 1) of powerful uniform rooted trees with a total of n-1 nodes.

LINKS

Table of n, a(n) for n=1..20.

Gus Wiseman, All 35 powerful uniform rooted trees with 11 nodes.

EXAMPLE

The a(8) = 12 powerful uniform rooted trees:

  (((((((o)))))))

  ((((((oo))))))

  (((((o)(o)))))

  ((((o))((o))))

  (((((ooo)))))

  (((o)(o)(o)))

  ((((oooo))))

  (((oo)(oo)))

  ((oo(o)(o)))

  (((ooooo)))

  ((oooooo))

  (ooooooo)

MATHEMATICA

rurt[n_]:=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[rurt/@ptn]], Or[Length[#]==1, And[Min@@Length/@Split[#]>=2, SameQ@@Length/@Split[#]]]&], {ptn, IntegerPartitions[n-1]}]];

Table[Length[rurt[n]], {n, 15}]

CROSSREFS

Cf. A000081, A003238, A072774, A317705, A317707, A317710, A317717, A317718, A318611, A318612, A318690, A318691, A318692.

Sequence in context: A033159 A199366 A332275 * A083710 A127524 A117086

Adjacent sequences:  A318686 A318687 A318688 * A318690 A318691 A318692

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 31 2018

STATUS

approved

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Last modified April 5 13:02 EDT 2020. Contains 333241 sequences. (Running on oeis4.)