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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =4a(6) =6a(7) =9a(8) =13a(9) =20a(10) =31a(11) =48a(12) =70a(13) =108a(14) =165a(15) =250a(16) =379a(17) =575a(18) =875a(19) =1332a(20) =2017a(21) =3066a(22) =4661a(23) =7076a(24) =10751a(25) =16328a(26) =24801a(27) =37684a(28) =57229a(29) =86931