Motion sequence data comprise a chronologically organized recording of a series of movements or actions carried out by a human being. Motion patterns found in such data holds significance for research and applications across multiple fields. In recent years, various feature representation techniques have been proposed to carry out sequence analysis. However, many of these methods have not fully uncovered the correlations between elements in sequences nor the internal interrelated structures among different dimensions, which are crucial to the recognition of motion patterns. This study proposes a novel Adaptive Sequence Coding (ASC) feature representation with ensemble hidden Markov models for motion sequence analysis. The ASC adopts the dual symbolization integrating first-order differential symbolization and event sequence encoding to effectively represent individual motion sequences. Subsequently, an adaptive boost algorithm based on a hidden Markov model is presented to distinguish the coded sequence data into different motion patterns. The experimental results on several publicly available datasets demonstrate that the proposed methodology outperforms other competing techniques. Meanwhile, ablation studies conducted on ASC and the adaptive boost approach further verify their significant potential in motion sequence analysis.