A347752 Orders of additive cubes in the tribonacci word A080843.

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

Table of n, a(n) for n=1..67.

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

Cf. A080843, A345717.

Sequence in context: A274429 A050618 A093579 * A060832 A341292 A047297

Adjacent sequences: A347749 A347750 A347751 * A347753 A347754 A347755

Keyword

nonn

Author

Jeffrey Shallit, Sep 18 2021

Status

approved