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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =2a(7) =2a(8) =3a(9) =4a(10) =4a(11) =6a(12) =7a(13) =9a(14) =11a(15) =14a(16) =16a(17) =22a(18) =26a(19) =33a(20) =40a(21) =53a(22) =62a(23) =82a(24) =97a(25) =127a(26) =151a(27) =198a(28) =234a(29) =309