Number of lone-child-avoiding rooted semi-identity trees with n vertices.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =2a(5) =3a(6) =5a(7) =9a(8) =16a(9) =30a(10) =55a(11) =105a(12) =200a(13) =388a(14) =754a(15) =1483a(16) =2923a(17) =5807a(18) =11575a(19) =23190a(20) =46608a(21) =94043a(22) =190287a(23) =386214a(24) =785831a(25) =1602952a(26) =3276845a(27) =6712905a(28) =13778079a(29) =28330583