Testing network protocol implementations is critical for ensuring the reliability, security, and interoperability of distributed systems. Faults in protocol behavior can lead to vulnerabilities and system failures, especially in real-time and mission-critical applications. A common approach to protocol testing involves constructing Markovian models that capture the state transitions and expected behaviors of the protocol. However, building such models typically requires significant domain expertise and manual effort, making the process time-consuming and difficult to scale across diverse protocols and implementations. We propose a novel method that leverages large language models (LLMs) to automatically generate sequences for testing network protocol implementations. Our approach begins by defining the full set of possible protocol states, from which the LLM selects a subset to model the target implementation. Using this state-based model, we prompt the LLM to generate code that produces sequences of states. This program serves as a protocol-specific sequences generator. The sequences generator then generates test inputs to call the protocol implementation under various conditions. We evaluated our approach on three widely used network protocol implementations and successfully identified 12 previously unknown vulnerabilities. We have reported them to the respective developers for confirmation. This demonstrates the practical effectiveness of our LLM-assisted fuzzing framework in uncovering real-world security issues.