Length of n-th iterate of the mapping 00->0010, 01->100, 10->001 in A289165.

Terms

a(0) =2a(1) =4a(2) =7a(3) =12a(4) =20a(5) =34a(6) =57a(7) =96a(8) =163a(9) =277a(10) =472a(11) =803a(12) =1368a(13) =2328a(14) =3963a(15) =6745a(16) =11481a(17) =19542a(18) =33260a(19) =56612a(20) =96369a(21) =164036a(22) =279208a(23) =475288a(24) =809027a(25) =1377074a(26) =2344072a(27) =3990031a(28) =6791680a(29) =11560716