

A051042


Number of ternary cubefree words of length n.


2



1, 3, 9, 24, 66, 180, 486, 1314, 3558, 9606, 25956, 70134, 189462, 511866, 1382880, 3735888, 10092762, 27266340, 73661610
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..18.
A. M. Shur, Growth properties of powerfree languages, Computer Science Review, Vol. 6 (2012), 187208.
A. M. Shur, Numerical values of the growth rates of powerfree languages, arXiv:1009.4415 [cs.FL], 2010.
Eric Weisstein's World of Mathematics, Cubefree Word.


FORMULA

Let L = lim a(n)^(1/n); then L exists since a(n) is submultiplicative. 2.7015614 < L < 2.7015616 (Shur 2012); the gap between the bounds can be made less than any given constant.  Arseny Shur, Apr 27 2015


EXAMPLE

There are 81 ternary words of length 4. Five of them contain the cube 000: 0000, 0001, 0002, 1000, 2000; same for 111 and 222. So, a(4)=813*5=66.  Arseny Shur, Apr 27 2015


CROSSREFS

Cf. A028445.
Sequence in context: A153582 A269461 A096168 * A121907 A179176 A118771
Adjacent sequences: A051039 A051040 A051041 * A051043 A051044 A051045


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


EXTENSIONS

More terms from Sascha Kurz, Mar 22 2002


STATUS

approved



