a(n) gives the length of A306211 after n generations.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =8a(5) =13a(6) =22a(7) =37a(8) =61a(9) =100a(10) =162a(11) =260a(12) =416a(13) =663a(14) =1053a(15) =1664a(16) =2617a(17) =4102a(18) =6416a(19) =10029a(20) =15684a(21) =24561a(22) =38531a(23) =60560a(24) =95334a(25) =150238a(26) =236878a(27) =373449a(28) =588441a(29) =926449