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

Offset: 1

Author

Christian G. Bower, Apr 29 2005

Keywords

• nonn
• eigen

Links

• Index entries for sequences related to mobiles

Crossrefs

Cf. A032200.

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