

A086713


A squarefree sequence: define a mapping from the set of strings over the alphabet {0,1,2} by f(0)=01201, f(1)=020121, f(2)=0212021 and f of the concatenation of s and t is the concatenation of f(s) and f(t). Then each of 0, f(0), f(f(0)), ... is an initial substring of the next; their limit is the infinite sequence given above.


0



0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0
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OFFSET

0,3


COMMENTS

f is a "squarefree morphism"; i.e. f(s) is squarefree iff s is squarefree.
For any i>0, f^i(0) has the same number of 0's and 1's and one less 2. The length of f^i(0) is A083066(i) = (4*6^i + 1)/5.


REFERENCES

Jean Berstel and Christophe Reutenauer, Squarefree words, p. 31.
M. Lothaire, Combinatorics on Words, Cambridge University Press, 1997.


LINKS

Table of n, a(n) for n=0..104.


EXAMPLE

f(f(0))=01201020121021202101201020121


MATHEMATICA

f[s_] := Flatten[{{0, 1, 2, 0, 1}, {0, 2, 0, 1, 2, 1}, {0, 2, 1, 2, 0, 2, 1}}[[ #+1]]&/@s]; f[f[f[{0}]]]


CROSSREFS

Sequence in context: A194942 A129688 A309011 * A275730 A049771 A158944
Adjacent sequences: A086710 A086711 A086712 * A086714 A086715 A086716


KEYWORD

easy,nonn


AUTHOR

Claude Lenormand (claude.lenormand(AT)free.fr), Jul 29 2003


EXTENSIONS

Edited by Dean Hickerson, Oct 19 2003


STATUS

approved



