A133235 - OEIS

%I #8 May 25 2013 23:55:31

%S 22,2222,22211222,22211222211222,222112222112211222211222,

%T 2221122221122112222112222112211222211222,

%U 222112222112211222211222211221122221122112222112222112211222211222

%N Numerical encoding of a series of binary words generated by a recurrence - see comments.

%C The sequence of words is bb, bbbb, bbbaabbb, bbbaabbbbaabbb, bbbaabbbbaabbaabbbbaabbb, ... given by the rule that the n-th word consists of the (n-1)st word, followed by the inverse of the (n-3)rd word, followed by the (n-1)st word.

%C Here a (or 1) and 2 (or b) represent the respective matrices

%C [1 1] [2 1]

%C [1 0] [1 0]

%C arising in the study of Markov numbers (A002559) - see link.

%C Question: Can this substitution-deletion system be described by a simple morphism of the type shown in A008352?

%H Tom Ace, <a href="http://www.minortriad.com/mmat.html">Calculating Markoff numbers with matrices</a>

%e a(4) = bbbaabbbbaabbaabbbbaabbb, a(2) = bbbaabbb, so a(5) = bbbaabbbbaabbaabbbbaabbb (bbbaabbb)^(-1) bbbaabbbbaabbaabbbbaabbb = bbbaabbbbaabbaabbbbaabbbbaabbaabbbbaabbb

%Y Cf. A002559, A008352, A003849.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Oct 14 2007, based on an email message from _James Propp_, Jan 28 2005