A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences satisfy similar closure properties as $C$-finite sequences. In particular, they form a difference ring. In this paper we present new techniques for performing these closure properties of $C^2$-finite sequences. These methods also allow us to derive order bounds which were not known before. Additionally, they provide more insight in the effectiveness of these computations. The results are based on the exponent lattice of algebraic numbers. We present an iterative algorithm which can be used to compute bases of such lattices.

翻译：如果符合以恒定系数的线性重现,则称为 " $C$-fite " 序列。我们研究以美元-Fite系数满足线性重现的序列。最近,我们发现,这类$C$2美元-fite序列满足了类似于C$-fite序列的封闭特性。特别是,它们形成了一个差异环。在本文中,我们介绍了用来进行这些封闭特性的新技术,即$C$2美元-fite序列。这些方法还使我们能够得出以前所不知道的定序界限。此外,它们提供了对这些计算效力的更多了解。结果基于代数的引力拉蒂斯。我们提出了一个迭代算法,可用来计算这些拉蒂克的基数。