A345717 -id:A345717 - cp's OEIS frontend

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

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Jeffrey Shallit, Sep 18 2021

nonn

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).

			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)

Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti, Additive word complexity and Walnut, arXiv:2410.02409 [math.CO], 2024. See p. 17.

Cf. A080843, A345717.

cp's OEIS Frontend

A347752 Orders of additive cubes in the tribonacci word A080843.

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