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A093370
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Start with any initial string of n numbers s(1), ..., s(n), with s(1) = 2, other s(i)'s = 2 or 3 (so there are 2^(n-1) starting strings). The rule for extending the string is this as follows: To get s(n+1), write the string s(1)s(2)...s(n) as xy^k for words x and y (where y has positive length) and k is maximized, i.e. k = the maximal number of repeating blocks at the end of the sequence. Then a(n) = number of starting strings for which k > 1.
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4
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0, 1, 2, 5, 10, 22, 44, 91, 182, 369, 738, 1486, 2972, 5962, 11924, 23884, 47768, 95607, 191214, 382568, 765136, 1530552, 3061104, 6122765, 12245530, 24492171, 48984342, 97970902, 195941804, 391888040
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
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FORMULA
| Equals A121880(n)/2, or 2^(n-1) - A122536(n)/2.
a(n)/2^(n-1) seems to converge to a number around 0.73.
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EXAMPLE
| For n=2 there are 2 starting strings, 22 and 23 and only the first has k>1.
For n=4 there are 8 starting strings, but only 5 have k>1, namely 2222, 2233, 2322, 2323, 2333.
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CROSSREFS
| Cf. A093371, A093369, A090822, A122536, A121880.
Sequence in context: A097096 A073777 A026633 * A094537 A135098 A045621
Adjacent sequences: A093367 A093368 A093369 * A093371 A093372 A093373
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 28 2004
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EXTENSIONS
| More terms from Guy P. Srinivasan (srinivgp(AT)gmail.com), via A122536, Sep 18 2006
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