Number of integers in n-th generation of tree T(1/4) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =2a(7) =2a(8) =2a(9) =4a(10) =4a(11) =4a(12) =5a(13) =8a(14) =8a(15) =9a(16) =12a(17) =16a(18) =17a(19) =21a(20) =27a(21) =32a(22) =37a(23) =47a(24) =57a(25) =67a(26) =82a(27) =102a(28) =121a(29) =145