Number of integers in n-th generation of tree T(3^(-1/3)) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =2a(7) =2a(8) =2a(9) =3a(10) =3a(11) =4a(12) =5a(13) =6a(14) =7a(15) =9a(16) =11a(17) =12a(18) =16a(19) =18a(20) =23a(21) =28a(22) =33a(23) =41a(24) =49a(25) =61a(26) =72a(27) =89a(28) =107a(29) =130