A032200 Number of rooted compound windmills (mobiles) of n nodes.

1, 1, 2, 4, 9, 20, 51, 128, 345, 940, 2632, 7450, 21434, 62174, 182146, 537369, 1596133, 4767379, 14312919, 43162856, 130695821, 397184252, 1211057426, 3703794849, 11358759346, 34923477315, 107627138308, 332404636811

Offset

1,3

Comments

Also the number of locally necklace plane trees with n nodes, where a plane tree is locally necklace if the sequence of branches directly under any given node is lexicographically minimal among its cyclic permutations. - Gus Wiseman, Sep 05 2018

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 241 (3.3.84).

Links

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

C. G. Bower, Transforms (2)

Index entries for sequences related to mobiles

Formula

Shifts left under "CIK" (necklace, indistinct, unlabeled) transform.

Example

From Gus Wiseman, Sep 05 2018: (Start)
The a(5) = 9 locally necklace plane trees:
  ((((o))))
  (((oo)))
  ((o(o)))
  (o((o)))
  ((o)(o))
  ((ooo))
  (o(oo))
  (oo(o))
  (oooo)
(End)

Mathematica

neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
neckplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[neckplane/@c], neckQ], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[neckplane[n]], {n, 10}] (* Gus Wiseman, Sep 05 2018 *)

Prog

(PARI)
CIK(p, n)={sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d)))}
seq(n)={my(p=O(1)); for(i=1, n, p=1+CIK(x*p, i)); Vec(p)} \\ Andrew Howroyd, Jun 20 2018

Crossrefs

Cf. A029768, A038037, A055340.

Cf. A000108, A007853, A032171, A254040, A304173, A304175, A317852.

Sequence in context: A027881 A002861 A363203 * A130969 A264293 A370315

Adjacent sequences: A032197 A032198 A032199 * A032201 A032202 A032203

Keyword

nonn,eigen

Author

Christian G. Bower

Status

approved