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^(n-1) 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.

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

Offset: 1

Author

N. J. A. Sloane, Apr 28 2004

Keywords

• nonn

Comments

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

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].
• Index entries for sequences related to curling numbers

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.

Formula

a(n) = 2^(n-1) - A093370(n).

Extensions

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