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Orders of additive cubes in the tribonacci word A080843.
1

%I #30 Oct 24 2024 15:09:33

%S 3,4,6,7,10,11,13,14,16,17,18,20,21,23,24,26,27,30,31,33,34,37,38,40,

%T 41,42,43,44,45,47,48,50,51,54,55,57,58,60,61,62,63,64,65,67,68,70,71,

%U 74,75,77,78,79,81,82,84,85,86,87,88,89,91,92,94,95,97,98,99

%N Orders of additive cubes in the tribonacci word A080843.

%C An additive cube is three consecutive blocks of the same length and same sum.

%C There is a tribonacci automaton of 4927 states recognizing the set of these orders (in tribonacci representation).

%H Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti, <a href="https://arxiv.org/abs/2410.02409">Additive word complexity and Walnut</a>, arXiv:2410.02409 [math.CO], 2024. See p. 17.

%e 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)

%Y Cf. A080843, A345717.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Sep 18 2021