a(n+1) = a(n)+a(a(a(..(n-1)..))), depth [ n/2 ].

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =1a(5) =1a(6) =2a(7) =3a(8) =4a(9) =5a(10) =5a(11) =5a(12) =6a(13) =7a(14) =8a(15) =9a(16) =9a(17) =9a(18) =10a(19) =11a(20) =11a(21) =11a(22) =12a(23) =13a(24) =14a(25) =15a(26) =15a(27) =15a(28) =16a(29) =17