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%I #13 Oct 09 2017 08:27:04
%S 1,1,1,2,3,6,14,30,68,159,381,914,2238,5508,13701,34288,86401,218818,
%T 557067,1424083,3655221,9414642,24328133,63049458,163844470,426831429,
%U 1114496370,2916228670,7645777113,20082543578,52839735409,139251228967
%N Mobiles (cycle rooted trees) where no branch is identical to its adjacent neighbor.
%H <a href="/index/Mo#mobiles">Index entries for sequences related to mobiles</a>
%F Shifts left under CycleBG transform.
%F CycleBG transform T(A) = invMOEBIUS(invEULER(Carlitz(A)) + A(x^2) - A) + A.
%F Carlitz transform T(A(x)) has g.f. 1/(1-sum(k>0, (-1)^(k+1)*A(x^k))).
%F 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
%Y Cf. A032200.
%K nonn,eigen
%O 1,4
%A _Christian G. Bower_, Apr 29 2005
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