Number of real integers in n-th generation of tree T(i) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =10a(7) =19a(8) =33a(9) =62a(10) =112a(11) =212a(12) =394a(13) =751a(14) =1419a(15) =2719a(16) =5193a(17) =10002a(18) =19254a(19) =37258a(20) =72132a(21) =140108a(22) =272368a(23) =530646a(24) =1034798a(25) =2021127a(26) =3951147a(27) =7733421a(28) =15148711a(29) =29702087