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A106364 Mobiles (cycle rooted trees) where no branch is identical to its adjacent neighbor. 1
1, 1, 1, 2, 3, 6, 14, 30, 68, 159, 381, 914, 2238, 5508, 13701, 34288, 86401, 218818, 557067, 1424083, 3655221, 9414642, 24328133, 63049458, 163844470, 426831429, 1114496370, 2916228670, 7645777113, 20082543578, 52839735409, 139251228967 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..32.

Index entries for sequences related to mobiles

FORMULA

Shifts left under CycleBG transform.

CycleBG transform T(A) = invMOEBIUS(invEULER(Carlitz(A)) + A(x^2) - A) + A.

Carlitz transform T(A(x)) has g.f. 1/(1-sum(k>0, (-1)^(k+1)*A(x^k))).

General formula for the CycleBG transform: T(A)(x) = A(x) - Sum_{k>=0} A(x^{2k+1}) + Sum_{k>=1} (phi(k)/k)*log(Carlitz(A)(x^k)). For a proof, see the links in the documentation of sequence A106368. - Petros Hadjicostas, Oct 08 2017

CROSSREFS

Cf. A032200.

Sequence in context: A250022 A322141 A240749 * A211931 A264078 A006444

Adjacent sequences:  A106361 A106362 A106363 * A106365 A106366 A106367

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Apr 29 2005

STATUS

approved

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Last modified May 21 19:00 EDT 2019. Contains 323444 sequences. (Running on oeis4.)