Number of integers in n-th generation of tree T(-5/2) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =4a(6) =6a(7) =8a(8) =12a(9) =19a(10) =28a(11) =42a(12) =63a(13) =95a(14) =145a(15) =212a(16) =321a(17) =479a(18) =723a(19) =1080a(20) =1622a(21) =2436a(22) =3652a(23) =5472a(24) =8212a(25) =12309a(26) =18488a(27) =27718a(28) =41599a(29) =62370