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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =14a(7) =30a(8) =68a(9) =159a(10) =381a(11) =914a(12) =2238a(13) =5508a(14) =13701a(15) =34288a(16) =86401a(17) =218818a(18) =557067a(19) =1424083a(20) =3655221a(21) =9414642a(22) =24328133a(23) =63049458a(24) =163844470a(25) =426831429a(26) =1114496370a(27) =2916228670a(28) =7645777113a(29) =20082543578