  Linear recurrent sequences are those whose elements are defined as linear
combinations of preceding elements, and finding relations of recurrences is a
fundamental problem in computer algebra. In this paper, we focus on sequences
whose elements are vectors over the ring $\mathbb{A} = \mathbb{K}[x]/(x^d)$ of
truncated polynomials. We present three methods for finding the ideal of
canceling polynomials: a Berlekamp-Massey-like approach due to Kurakin, one
which computes the kernel of some block-Hankel matrix over $\mathbb{A}$ via a
minimal approximant basis, and one based on bivariate Pad\'e approximation. We
propose complexity improvements for the first two methods, respectively by
avoiding the computation of redundant sequence generators and by exploiting the
Hankel structure to compress the approximation instance. We then observe these
improvements in our empirical results through a C++ implementation. Finally we
discuss applications to the computation of minimal polynomials and determinants
of sparse matrices over $\mathbb{A}$.
