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A214217 List of singular subwords (or factors) of the Fibonacci word A003842. 2
2, 11, 212, 11211, 21211212, 1121121211211, 212112121121121211212, 1121121211211212112121121121211211, 2121121211211212112121121121211211212112121121121211212, 11211212112112121121211211212112112121121211211212112121121121211211212112121121121211211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complementing the first and last digits of each term gives (essentially) A214216.

REFERENCES

Kalle Saari, Periods of factors of the Fibonacci word, Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland (2001), citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.992

K. Saari, Periods of factors of the Fibonacci word, in Proceedings of the Sixth International Conference on Words (WORDS’07). Institut de Mathématiques de Luminy (2007) 273-279.

Wen, Z.-X.; Wen, Z.-Y. Some properties of the singular words of the Fibonacci word, European J. Combin. 15 (1994), 587-598.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

a(0)=2, a(1)=11, a(2)=212; thereafter a(n)=the concatenation of a(n-2), a(n-3), and a(n-2).

MATHEMATICA

nxt[{a_, b_, c_}]:={b, c, FromDigits[Join[Flatten[IntegerDigits/@{b, a, b}]]]}; NestList[nxt, {2, 11, 212}, 10][[All, 1]] (* Harvey P. Dale, May 24 2018 *)

CROSSREFS

Cf. A003842, A214216.

Sequence in context: A036229 A104337 A283512 * A042805 A088639 A269710

Adjacent sequences:  A214214 A214215 A214216 * A214218 A214219 A214220

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 10 2012

EXTENSIONS

Formula clarified by Harvey P. Dale, May 24 2018

STATUS

approved

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)