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%I #7 Mar 30 2012 17:37:15
%S 1,1,1,2,4,10,28,77,221,650,1951,5920,18211,56509,176919,557786,
%T 1769966,5647568,18110734,58335561,188658338,612337013,1994058293,
%U 6513153445,21332562178,70048092196,230550762108,760462920317
%N Number of rooted planar trees in which no branch is identical to its adjacent neighbor.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f.: x+x*B(x) where B(x) is g.f. of CycleBG transform of A106361.
%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))).
%Y Cf. A003239, A106363.
%K nonn
%O 1,4
%A _Christian G. Bower_, Apr 29 2005