OFFSET
1
COMMENTS
The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289010.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first seven iterates of the mapping:
00
0010
0010011
00100110011
00100110010110011
00100110010110010010110011
0010011001011001001011001001001110110011
MATHEMATICA
z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "011"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A289007 *)
Flatten[Position[st, 0]] (* A289008 *)
Flatten[Position[st, 1]] (* A289009 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289010 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 26 2017
STATUS
approved