Number of integers in n-th generation of tree T(-1/4) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =2a(7) =3a(8) =4a(9) =6a(10) =7a(11) =9a(12) =12a(13) =17a(14) =22a(15) =29a(16) =38a(17) =51a(18) =68a(19) =90a(20) =119a(21) =158a(22) =209a(23) =277a(24) =368a(25) =489a(26) =648a(27) =858a(28) =1137a(29) =1509