Length of n-th iterate of the mapping 00->0010, 01->001, 10->000, starting with 00.

Terms

a(0) =2a(1) =4a(2) =7a(3) =12a(4) =22a(5) =39a(6) =68a(7) =121a(8) =213a(9) =379a(10) =676a(11) =1206a(12) =2155a(13) =3832a(14) =6823a(15) =12156a(16) =21658a(17) =38584a(18) =68716a(19) =122402a(20) =218016a(21) =388317a(22) =691583a(23) =1231599a(24) =2193224a(25) =3905575a(26) =6954709a(27) =12384775a(28) =22053977a(29) =39271946