A106364 - OEIS

A106364

Mobiles (cycle rooted trees) where no branch is identical to its adjacent neighbor.

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

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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 A240749 A331684 * A211931 A264078 A006444

Adjacent sequences: A106361 A106362 A106363 * A106365 A106366 A106367

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Apr 29 2005

STATUS

approved