Number of integers in n-th generation of tree T(2/3) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =3a(7) =4a(8) =5a(9) =6a(10) =9a(11) =11a(12) =14a(13) =19a(14) =25a(15) =32a(16) =43a(17) =56a(18) =73a(19) =97a(20) =128a(21) =167a(22) =222a(23) =292a(24) =384a(25) =507a(26) =670a(27) =882a(28) =1165a(29) =1539