|
| |
|
|
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 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
|
|
|
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
|
| |
|
|
