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

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =0a(5) =1a(6) =1a(7) =2a(8) =2a(9) =4a(10) =6a(11) =10a(12) =16a(13) =27a(14) =44a(15) =74a(16) =123a(17) =209a(18) =353a(19) =602a(20) =1026a(21) =1760a(22) =3019a(23) =5203a(24) =8977a(25) =15538a(26) =26930a(27) =46792a(28) =81415a(29) =141939