%I #8 Sep 25 2017 04:09:41

%S 2,4,7,12,20,34,58,99,169,288,491,837,1428,2437,4159,7099,12118,20686,

%T 35313,60283,102909,175676,299897,511955,873961,1491944,2546908,

%U 4347844,7422234,12670546,21629975,36924676,63034365,107606391,183695599

%N Length of n-th iterate of the mapping 00->0010, 10->010, 1-->001, starting with 00.

%t z = 34; (* number of iterations *)

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "001"}]

%t TableForm[Table[w[n], {n, 0, 4}]]

%t Table[StringLength[w[n]], {n, 0, z}] (* A289028 *)

%Y Cf. A289025.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Jul 10 2017