

A093371


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^(n1) starting strings). The rule for extending the string is this as follows: To get s(n+1), write the string s(1)s(2)...s(n) 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. Then a(n) = number of starting strings for which k = 1.


17



1, 1, 2, 3, 6, 10, 20, 37, 74, 143, 286, 562, 1124, 2230, 4460, 8884, 17768, 35465, 70930, 141720, 283440, 566600, 1133200, 2265843, 4531686, 9062261, 18124522, 36246826, 72493652, 144982872
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OFFSET

1,3


COMMENTS

See A122536 for many more terms.  N. J. A. Sloane, Oct 25 2012


LINKS

Table of n, a(n) for n=1..30.
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].
Index entries for sequences related to curling numbers


FORMULA

a(n) = 2^(n1)  A093370(n).


CROSSREFS

Cf. A093370, A093369, A090822, A216955, A216956.
Equals A122536/2.  N. J. A. Sloane, Sep 25 2012
Different from, but easily confused with, A007148 and A045690.
Sequence in context: A158291 A045690 A007148 * A003214 A331693 A123423
Adjacent sequences: A093368 A093369 A093370 * A093372 A093373 A093374


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 28 2004


EXTENSIONS

More terms from N. J. A. Sloane, Sep 26 2012


STATUS

approved



