Number of integers in n-th generation of tree T(2^(-1/3)) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =2a(7) =3a(8) =3a(9) =5a(10) =6a(11) =8a(12) =9a(13) =13a(14) =17a(15) =22a(16) =27a(17) =36a(18) =47a(19) =61a(20) =77a(21) =101a(22) =132a(23) =171a(24) =219a(25) =285a(26) =370a(27) =480a(28) =619a(29) =803