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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

A. M. Shur, Growth properties of power-free languages, Computer Science Review, Vol. 6 (2012), 187-208.

A. M. Shur, Numerical values of the growth rates of power-free 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)=81-3*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

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)