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arXiv · 1606.02161

The numbers of distinct and repeated squares and cubes in the Tribonacci sequence

Huang Yuke·Wen Zhiying
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Abstract

The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $\sigma(a,b,c)=(ab,ac,a)$. The main result is twofold: (1) we give the explicit expressions of the numbers of distinct squares and cubes in $\mathbb{T}[1,n]$ (the prefix of $\mathbb{T}$ of length $n$); (2) we give algorithms for counting the number of repeated squares and cubes in $\mathbb{T}[1,n]$ for all $n$; then get explicit expressions for some special $n$ such as $n=t_m$ (the Tribonacci number).

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Huang Yuke, Wen Zhiying. 2016-06-07. The numbers of distinct and repeated squares and cubes in the Tribonacci sequence. https://arxiv.org/abs/1606.02161

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