Number of lone-child-avoiding locally disjoint unlabeled rooted trees with n vertices.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =2a(5) =3a(6) =6a(7) =9a(8) =16a(9) =26a(10) =45a(11) =72a(12) =124a(13) =201a(14) =341a(15) =561a(16) =947a(17) =1571a(18) =2651a(19) =4434a(20) =7496a(21) =12631a(22) =21423a(23) =36332a(24) =61910a(25) =105641a(26) =180924a(27) =310548a(28) =534713a(29) =923047