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A093371
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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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3
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1, 1, 2, 3, 6, 10, 20, 37, 74, 143, 286, 562, 1124, 2230, 4460, 8884, 17768, 35465, 70930, 141720
(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
| a(n) = 2^(n-1) - A093370(n).
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CROSSREFS
| Cf. A093370, A093369, A090822.
Sequence in context: A158291 A045690 A007148 * A003214 A123423 A005195
Adjacent sequences: A093368 A093369 A093370 * A093372 A093373 A093374
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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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