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Search: id:A133235
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| A133235 |
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Numerical encoding of a series of binary words generated by a recurrence - see comments. |
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+0
3
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| 22, 2222, 22211222, 22211222211222, 222112222112211222211222, 2221122221122112222112222112211222211222, 222112222112211222211222211221122221122112222112222112211222211222
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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?
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LINKS
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James Propp, Calculating Markoff numbers with matrices
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EXAMPLE
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a(4) = bbbaabbbbaabbaabbbbaabbb, a(2) = bbbaabbb, so a(5) = bbbaabbbbaabbaabbbbaabbb (bbbaabbb)^(-1) bbbaabbbbaabbaabbbbaabbb = bbbaabbbbaabbaabbbbaabbbbaabbaabbbbaabbb
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CROSSREFS
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Cf. A002559, A008352, A003849.
Sequence in context: A033526 A078399 A046445 this_sequence A114449 A069221 A069222
Adjacent sequences: A133232 A133233 A133234 this_sequence A133236 A133237 A133238
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 14 2007, based on an email message from James Propp, Jan 28 2005
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