Length of n-th iterate of the mapping 00->0010, 01->001, 10->011, starting with 00.

Terms

a(0) =2a(1) =4a(2) =7a(3) =11a(4) =17a(5) =26a(6) =40a(7) =61a(8) =92a(9) =137a(10) =203a(11) =299a(12) =437a(13) =634a(14) =915a(15) =1317a(16) =1891a(17) =2708a(18) =3869a(19) =5520a(20) =7869a(21) =11209a(22) =15954a(23) =22693a(24) =32268a(25) =45874a(26) =65203a(27) =92655a(28) =131644a(29) =187026