

A133235


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


2



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

0,1


COMMENTS

The sequence of words is bb, bbbb, bbbaabbb, bbbaabbbbaabbb, bbbaabbbbaabbaabbbbaabbb, ... given by the rule that the nth word consists of the (n1)st word, followed by the inverse of the (n3)rd word, followed by the (n1)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 substitutiondeletion system be described by a simple morphism of the type shown in A008352?


LINKS

Table of n, a(n) for n=0..6.
Tom Ace, Calculating Markoff numbers with matrices


EXAMPLE

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


CROSSREFS

Cf. A002559, A008352, A003849.
Sequence in context: A183488 A253128 A046445 * A114449 A069221 A069222
Adjacent sequences: A133232 A133233 A133234 * A133236 A133237 A133238


KEYWORD

nonn


AUTHOR

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


STATUS

approved



