A133235 Numerical encoding of a series of binary words generated by a recurrence - see comments.

22, 2222, 22211222, 22211222211222, 222112222112211222211222, 2221122221122112222112222112211222211222, 222112222112211222211222211221122221122112222112222112211222211222

Offset: 0

Author

N. J. A. Sloane, Oct 14 2007, based on an email message from James Propp, Jan 28 2005

Keywords

• nonn

Comments

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.

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

[1 1] [2 1]

[1 0] [1 0]

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

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

Examples

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

Links

• Tom Ace, Calculating Markoff numbers with matrices

Crossrefs

Cf. A002559, A008352, A003849.