

A094005


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.


4



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, 3991605129, 8251710234, 17040335019, 35154540729, 72456654860, 149208536983
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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 (k is the curling number of s(1)s(2)...s(i)). 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.
See A094004 for more terms.  N. J. A. Sloane, Dec 25 2012


LINKS

Table of n, a(n) for n=1..32.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A SlowGrowing 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 SlowGrowing 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


FORMULA

Equals A216813(n) + n*2^n.  N. J. A. Sloane, Sep 26 2012
A093369 is closely related.


CROSSREFS

Cf. A090822, A093370, A093371, A094004, A216813.
Sequence in context: A023664 A023622 A119438 * A190154 A187830 A115058
Adjacent sequences: A094002 A094003 A094004 * A094006 A094007 A094008


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 31 2004.


EXTENSIONS

a(27)a(31) from N. J. A. Sloane, Sep 19 2012


STATUS

approved



