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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

Lars Blomberg, Table of n, a(n) for n = 1..37

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.

Index entries for sequences related to Gijswijt's sequence

Index entries for sequences related to curling numbers

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

Cf. A090822, A093370, A093371, A094004, A094005.

Sequence in context: A069166 A184393 A281707 * A130443 A294655 A005515

Adjacent sequences:  A093366 A093367 A093368 * A093370 A093371 A093372

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 October 22 18:17 EDT 2019. Contains 328319 sequences. (Running on oeis4.)