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)
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
KEYWORD
nonn,eigen
AUTHOR
STATUS
approved