%I A093369
%S A093369 1,6,14,42,98,242,552,1394,2935,6471,14006,30060,64223,136914,
%T A093369 290224,613509,1292567,2717311,5696864,11920124
%N A093369 a(n) = sum of lengths of strings that can be generated by any starting 
               string of n 2's and 3's that starts with a 2, using the rule described 
               in the Comments lines.
%C A093369 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:
%C A093369 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).
%C A093369 a(n) = sum of final length of string, summed over all 2^(n-1) starting 
               strings.
%H A093369 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and 
               A. R. Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. 
               Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A093369 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 
               [<a href="http://www.research.att.com/~njas/doc/gijs.pdf">pdf</a>
               , <a href="http://www.research.att.com/~njas/doc/gijs.ps">ps</a>].
%e A093369 a(3) = 14: the starting string, final string and length are as follows:
%e A093369 222 2223 4
%e A093369 223 223 3
%e A093369 232 232 3
%e A093369 233 2332 4, for a total of 4+3+3+4 = 14.
%Y A093369 Cf. A090822, A093370, A093371, A094004, A094005.
%Y A093369 Sequence in context: A134259 A069166 A015892 this_sequence A130443 A005515 
               A114705
%Y A093369 Adjacent sequences: A093366 A093367 A093368 this_sequence A093370 A093371 
               A093372
%K A093369 nonn,more
%O A093369 1,2
%A A093369 N. J. A. Sloane (njas(AT)research.att.com), Apr 28 2004