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A324764 Number of anti-transitive rooted identity trees with n nodes. 17
1, 1, 1, 1, 3, 4, 9, 20, 41, 89, 196, 443, 987, 2246, 5114, 11757, 27122, 62898, 146392, 342204, 802429, 1887882 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root. It is anti-transitive if the branches of the branches of the root are disjoint from the branches of the root.

Also the number of finitary sets S with n brackets where no element of an element of S is also an element of S. For example, the a(8) = 20 finitary sets are (o = {}):

  {{{{{{{o}}}}}}}

  {{{{{o,{o}}}}}}

  {{{{o,{{o}}}}}}

  {{{o,{{{o}}}}}}

  {{{o,{o,{o}}}}}

  {{{{o},{{o}}}}}

  {{o,{{{{o}}}}}}

  {{o,{{o,{o}}}}}

  {{o,{o,{{o}}}}}

  {{{o},{{{o}}}}}

  {{{o},{o,{o}}}}

  {{o,{o},{{o}}}}

  {o,{{{{{o}}}}}}

  {o,{{{o,{o}}}}}

  {o,{{o,{{o}}}}}

  {o,{{o},{{o}}}}

  {{o},{{{{o}}}}}

  {{o},{{o,{o}}}}

  {{o},{o,{{o}}}}

  {{{o}},{o,{o}}}

LINKS

Table of n, a(n) for n=1..22.

Gus Wiseman, The a(9) = 41 anti-transitive rooted identity trees.

EXAMPLE

The a(1) = 1 through a(7) = 9 anti-transitive rooted identity trees:

  o  (o)  ((o))  (((o)))  ((o(o)))   (((o(o))))   ((o(o(o))))

                          (o((o)))   ((o((o))))   (o((o(o))))

                          ((((o))))  (o(((o))))   ((((o(o)))))

                                     (((((o)))))  (((o)((o))))

                                                  (((o((o)))))

                                                  ((o)(((o))))

                                                  ((o(((o)))))

                                                  (o((((o)))))

                                                  ((((((o))))))

MATHEMATICA

idall[n_]:=If[n==1, {{}}, Select[Union[Sort/@Join@@(Tuples[idall/@#]&/@IntegerPartitions[n-1])], UnsameQ@@#&]];

Table[Length[Select[idall[n], Intersection[Union@@#, #]=={}&]], {n, 10}]

CROSSREFS

Cf. A000081, A004111, A276625, A279861, A290689, A304360, A306844 (non-identity version), A316500, A317787, A318185.

Cf. A324694, A324751, A324756, A324758, A324765, A324767, A324768, A324770, A324839, A324840, A324844.

Sequence in context: A247579 A282615 A049978 * A092763 A232955 A116868

Adjacent sequences:  A324761 A324762 A324763 * A324765 A324766 A324767

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 17 2019

EXTENSIONS

a(21)-a(22) from Jinyuan Wang, Jun 20 2020

STATUS

approved

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Last modified July 4 11:19 EDT 2020. Contains 335448 sequences. (Running on oeis4.)