Tribonacci数列的幂数
The numbers of powers in the Tribonacci sequence
摘要：
Tribonacci序列$\mathbb{T}$是置换$σ(a)=ab$、$σ(b)=ac$、$σ(c)=a$的不动点。长度为$n$的$\mathbb{T}$的前缀由$\mathbb{T}[1,n]$表示。主要结果有三个方面：（1）给出了$\mathbb{T}[1,n]$中不同正方形和立方体个数的显式表达式;（2）给出了$\mathbb{T}[1,n]$中重复正方形和立方体个数的计算算法;（3）讨论了$α\geq2$和$n\geq1$的$α$ -幂。
英文摘要：
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $σ(a)=ab$, $σ(b)=ac$, $σ(c)=a$. The prefix of $\mathbb{T}$ of length $n$ is denoted by $\mathbb{T}[1,n]$. The main result is threefold, we give: (1) explicit expressions of the numbers of distinct squares and cubes in $\mathbb{T}[1,n]$; (2) algorithms for counting the numbers of repeated squares and cubes in $\mathbb{T}[1,n]$; (3) a discussion about $α$-powers in $\mathbb{T}[1,n]$ for $α\geq2$ and $n\geq1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
