Length of n-th iterate of the mapping 00->0010, 01->100, 10->011 in A289165.

Terms

a(0) =2a(1) =4a(2) =7a(3) =11a(4) =17a(5) =25a(6) =38a(7) =57a(8) =85a(9) =126a(10) =185a(11) =271a(12) =396a(13) =576a(14) =835a(15) =1208a(16) =1745a(17) =2515a(18) =3622a(19) =5215a(20) =7509a(21) =10814a(22) =15583a(23) =22470a(24) =32423a(25) =46820a(26) =67651a(27) =97800a(28) =141457a(29) =204684