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%I #4 Jun 29 2017 14:56:19
%S 2,4,7,12,20,34,57,96,163,277,472,803,1368,2328,3963,6745,11481,19542,
%T 33260,56612,96369,164036,279208,475288,809027,1377074,2344072,
%U 3990031,6791680,11560716,19678465,33496200,57016621,97052630
%N Length of n-th iterate of the mapping 00->0010, 01->100, 10->001 in A289165.
%t z = 22; (* number of iterates *)
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "001"}];
%t st = ToCharacterCode[w[z]] - 48 ; (* A289165 *)
%t v = Table[StringLength[w[n]], {n, 0, 30}] (* A289168 *)
%Y Cf. A289165.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Jun 29 2017