Lenormand concatenated words on alphabet (x,y)

[Eric Angelini]

Hello SeqFan,

This is « Exercice 14 », there:
http://www.ai.univ-paris8.fr/~lenormand/chapitre1/1.1_Prolegomenes.pdf

My translation:

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No word of this sequence S of words on alphabet (x,y)
is produced by ordinated concatenation of the words 
appearing before:

x y yx yxx yxy yxxx yxxy yxyy yxxxx yxxxy yxxyx yxxyy yxyxx yxyyx yxyyy yxxxxx ...

... doing x=0 and y=1 gives:

0,1,10,100,101,1000,1001,1011,10000,10001,10010,10011,10100,10110,10111,100000

... which is in base 10:

0 1 2 4 5 8 9 11 16 17 18 19 20 22 23 32 ...

(...)
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... This seq. is not in the OEIS, if I'm not wrong.

My french is not good enough to understand how this 
seq. is produced, though :

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« Enumération et factorisation des mots sur (x,y) 
  comme fonction ordonnée des mots de S:

  (dans S, x est le seul mot dont la première lettre
  est x, aucun mot ne commence par yy, par contre tout
  mot de la forme yxi convient, et pour tout mot m de S
  distinct de x et y, my convient....)

x y
x.x x.y yx y.y
x.x.x x.x.y x.yx x.y.y yxx yxy y.yx y.y.y
x.x.x.x x.x.x.y x.x.yx x.x.y.y x.yxx x.yxy x.y.yx x.y.y.y yxxx yxxy yx.yx yxyy y.yxx
y.yxy y.y.yx y.y.y.y ... »

(...)
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Is this of interest ?

Best,
É.