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A094005
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a(n) = sum of lengths of strings that can be generated by any starting string of n 2's and 3's, using the rule described in the Comments lines.
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2
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2, 11, 30, 82, 199, 480, 1097, 2630, 5828, 12830, 27873, 60071, 128355, 273543, 580149, 1226626, 2584822, 5433676, 11392986, 23838396, 49776503, 103755527, 215904926, 448602871, 930771041, 1928682932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Start with any initial string of n numbers s(1), ..., s(n), all = 2 or 3 (so there are 2^n starting strings). The rule for extending the string is this:
To get s(i+1), write the string s(1)s(2)...s(i) 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 so far. Then s(i+1) = k if k >=2, but if k=1 you must stop (without writing down the 1).
a(n) = sum of final length of string, summed over all 2^n starting strings.
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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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CROSSREFS
| Cf. A090822, A093370, A093371, A094004.
Sequence in context: A023664 A023622 A119438 * A190154 A115058 A158295
Adjacent sequences: A094002 A094003 A094004 * A094006 A094007 A094008
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 31 2004
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