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A214217
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List of singular subwords (or factors) of the Fibonacci word A003842.
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2
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2, 11, 212, 11211, 21211212, 1121121211211, 212112121121121211212, 1121121211211212112121121121211211, 2121121211211212112121121121211211212112121121121211212, 11211212112112121121211211212112112121121211211212112121121121211211212112121121121211211
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Complementing the first and last digits of each term gives (essentially) A214216.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..10.
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FORMULA
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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).
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A003842, A214216.
Sequence in context: A036229 A104337 A283512 * A042805 A088639 A269710
Adjacent sequences: A214214 A214215 A214216 * A214218 A214219 A214220
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jul 10 2012
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EXTENSIONS
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Formula clarified by Harvey P. Dale, May 24 2018
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STATUS
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approved
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