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, 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

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: A356677 A309011 A365921 * A275730 A049771 A352514

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