A032027 - OEIS

A032027

Number of planted planar trees (n+1 nodes) where any 2 subtrees extending from the same node are different.

1, 1, 1, 3, 5, 13, 35, 95, 255, 715, 2081, 6003, 17645, 52127, 155863, 468129, 1415521, 4301055, 13134789, 40275109, 123970669, 382919917, 1186475687, 3686899725, 11487023793, 35876838669, 112304155021, 352276801491

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OFFSET

1,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

C. G. Bower, Transforms (2)

Index entries for sequences related to rooted trees

FORMULA

Shifts left under "AGK" (ordered, elements, unlabeled) transform.

EXAMPLE

From Gus Wiseman, Nov 15 2022: (Start)

The a(1) = 1 through a(6) = 13 ordered rooted identity trees (ranked by A358374):

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)))))

(End)

MATHEMATICA

aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];

Table[Length[Select[aot[n], FreeQ[#, _[__]?(!UnsameQ@@#&)]&]], {n, 1, 10}] (* Gus Wiseman, Nov 15 2022 *)

PROG

(PARI)

AGK(v)={apply(p->subst(serlaplace(y^0*p), y, 1), Vec(prod(k=1, #v, (1 + x^k*y + O(x*x^#v))^v[k])-1, -#v))}

seq(n)={my(v=[1]); for(i=2, n, v=concat([1], AGK(v))); v} \\ Andrew Howroyd, Sep 20 2018

CROSSREFS

The unordered version is A004111, ranked by A276625.

These trees (ordered rooted identity) are ranked by A358374.

Cf. A000081, A001190, A005043, A003238, A063895, A358377.

Sequence in context: A283844 A324783 A032009 * A360863 A005383 A306826

Adjacent sequences: A032024 A032025 A032026 * A032028 A032029 A032030

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower

STATUS

approved