Tribonacci数列中不同重复正方形和立方体的个数
The numbers of distinct and repeated squares and cubes in the Tribonacci sequence
摘要：
Tribonacci序列$\mathbb{T}$是置换$σ(a,b,c)=(ab,ac,a)$的不动点。主要结果有两个方面：（1）给出了长度为$n$的$\mathbb{T}$的前缀$\mathbb{T}[1,n]$中不同正方形和立方体个数的显式表达式;（2）对所有$n$给出了计算$\mathbb{T}[1,n]$中重复正方形和立方体个数的算法;并对某些特殊的$n$如$n=t_m$（Tribonacci数）给出了显式表达式。
英文摘要：
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $σ(a,b,c)=(ab,ac,a)$. 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).
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。
