

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
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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^(n1) 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^(n1) starting strings.


LINKS

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].


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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



