We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference of the two preceding terms where the pluses and minuses follow a certain pattern. In 2012, McLellan proved that if the pluses and minuses follow a periodic pattern and $G_n$ is the nth term of the resulting generalised Fibonacci sequence, then$\underset{n\to \infty }{\lim }|G_n{|}^{1/n}$ exists. We extend her results to recurrences of the form $G_{m+2}={\alpha }_m{G}_{m+1}\pm G_m$ if the choices of pluses and minuses, and of the ${\alpha }_m$ follow a balancing word type pattern.

我们研究特定结构的广义斐波那契数列的增长率。这些序列是通过为前两项选择两个实数来构建的，并且下一项始终是前两项的和或差，其中加号和减号遵循特定模式。2012 年，McLellan 证明，如果正负遵循周期性模式，并且$G_n$是所得广义斐波那契数列的第n项，则$\underset{n\to \infty }{\mathrm{林}}|G_n{|}^{1/n}$存在。我们将她的结果扩展到形式的重复$G_{米+2}={\alpha }_{米}{G}_{米+1}\pm G_{米}$ 如果优点和缺点的选择，以及 ${\alpha }_{米}$ 遵循平衡的字型模式。