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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. 6
1, 6, 14, 42, 98, 242, 552, 1394, 2935, 6471, 14006, 30060, 64223, 136914, 290224, 613509, 1292567, 2717311, 5696864, 11920124, 24889066, 51880008, 107954163, 224305440, 465388743, 964349526, 1995808823, 4125871527, 8520180124, 17577302639, 36228352911 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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:
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-1) starting strings.
LINKS
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan 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 Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102, Dec 25 2012.
B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
EXAMPLE
a(3) = 14: the starting string, final string and length are as follows:
222 2223 4
223 223 3
232 232 3
233 2332 4, for a total of 4+3+3+4 = 14.
CROSSREFS
Sequence in context: A134259 A069166 A184393 * A130443 A349835 A294655
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 28 2004
EXTENSIONS
a(21)-a(31) from Lars Blomberg, Jul 25 2017
STATUS
approved

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Last modified July 24 15:22 EDT 2024. Contains 374584 sequences. (Running on oeis4.)