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

Terms

a(0) =2a(1) =4a(2) =7a(3) =12a(4) =20a(5) =34a(6) =58a(7) =99a(8) =169a(9) =288a(10) =491a(11) =837a(12) =1428a(13) =2437a(14) =4159a(15) =7099a(16) =12118a(17) =20686a(18) =35312a(19) =60280a(20) =102903a(21) =175665a(22) =299877a(23) =511920a(24) =873900a(25) =1491838a(26) =2546724a(27) =4347527a(28) =7421690a(29) =12669614