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A347752
Orders of additive cubes in the tribonacci word A080843.
1
3, 4, 6, 7, 10, 11, 13, 14, 16, 17, 18, 20, 21, 23, 24, 26, 27, 30, 31, 33, 34, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 50, 51, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 70, 71, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87, 88, 89, 91, 92, 94, 95, 97, 98, 99
OFFSET
1,1
COMMENTS
An additive cube is three consecutive blocks of the same length and same sum.
There is a tribonacci automaton of 4927 states recognizing the set of these orders (in tribonacci representation).
LINKS
Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti, Additive word complexity and Walnut, arXiv:2410.02409 [math.CO], 2024. See p. 17.
EXAMPLE
The first few examples of additive cubes of different lengths in the tribonacci word are 020.101.020 (order 3), 2010.0102.0102 (order 4), and 102010.010201.010201 (order 6)
CROSSREFS
Sequence in context: A274429 A050618 A093579 * A060832 A341292 A047297
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Sep 18 2021
STATUS
approved