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) =2a(7) =4a(8) =5a(9) =7a(10) =10a(11) =14a(12) =17a(13) =23a(14) =33a(15) =43a(16) =61a(17) =82a(18) =111a(19) =150a(20) =202a(21) =278a(22) =376a(23) =516a(24) =694a(25) =941a(26) =1281a(27) =1731a(28) =2369a(29) =3208