Length of n-th iterate of the mapping 00->0010, 01->100, 10->000 in A289235.

Terms

a(0) =2a(1) =4a(2) =7a(3) =12a(4) =22a(5) =39a(6) =68a(7) =122a(8) =217a(9) =385a(10) =687a(11) =1224a(12) =2181a(13) =3895a(14) =6945a(15) =12363a(16) =22001a(17) =39161a(18) =69711a(19) =124107a(20) =220901a(21) =393356a(22) =700465a(23) =1247432a(24) =2221413a(25) =3955905a(26) =7044756a(27) =12545540a(28) =22340117a(29) =39782044