A036580 Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

0 is a, 1 is b and 2 is c. - Robert G. Wilson v, Jul 30 2018

References

• M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 26.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Marko Milosevic and Narad Rampersad, Squarefree words with interior disposable factors, arXiv:2007.03557 [math.CO], 2020.
• Michaël Rao, Michel Rigo, and Pavel Salimov, Avoiding 2-binomial squares and cubes, arXiv:1310.4743 [cs.FL], 2013.
• Michaël Rao, Michel Rigo, and Pavel Salimov, Avoiding 2-binomial squares and cubes, Theoretical Computer Science, Volume 572, 23 March 2015, Pages 83-91.

Crossrefs

A007413(n+1) - 1.

See A036577 for another version.

Programs

Mathematica

Nest[Flatten[# /. {0 -> {0, 1, 2}, 1 -> {0, 2}, 2 -> {1}}] &, {1}, 7] // Most (* Robert G. Wilson v, Jul 30 2018, corrected by Paolo Xausa, Jul 21 2025 *)
1 - Differences[ThueMorse[Range[0,100]]] (* Paolo Xausa, Jul 21 2025 *)