Number of integers in n-th generation of tree T(1/2) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =4a(6) =5a(7) =8a(8) =11a(9) =17a(10) =25a(11) =37a(12) =54a(13) =81a(14) =119a(15) =177a(16) =261a(17) =388a(18) =574a(19) =851a(20) =1260a(21) =1868a(22) =2767a(23) =4101a(24) =6077a(25) =9006a(26) =13347a(27) =19781a(28) =29315a(29) =43448