%I #4 Jun 29 2017 14:56:47

%S 2,4,7,11,17,25,38,57,85,126,185,271,396,576,835,1208,1745,2515,3622,

%T 5215,7509,10814,15583,22470,32423,46820,67651,97800,141457,204684,

%U 296265,428950,621218,899829,1303584,1888759,2736886,3966153,5747943,8330630,12074219

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

%t z = 41 ; (* number of iterations *)

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "011"}];

%t TableForm[Table[w[n], {n, 0, 6}]]

%t st = ToCharacterCode[w[z]] - 48 ; (* A289174 *)

%t Table[StringLength[w[n]], {n, 0, z}] (* A289177 *)

%Y Cf. A289174.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Jun 29 2017