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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =3a(7) =4a(8) =6a(9) =7a(10) =10a(11) =14a(12) =19a(13) =25a(14) =35a(15) =47a(16) =64a(17) =87a(18) =119a(19) =161a(20) =220a(21) =300a(22) =407a(23) =554a(24) =757a(25) =1028a(26) =1399a(27) =1908a(28) =2598a(29) =3534