Accurate battery modeling is essential for reliable state estimation in modern applications, such as predicting the remaining discharge time and remaining discharge energy in battery management systems. Existing approaches face several limitations: model-based methods require a large number of parameters; data-driven methods rely heavily on labeled datasets; and current physics-informed neural networks (PINNs) often lack aging adaptation, or still depend on many parameters, or continuously regenerate states. In this work, we propose SeqBattNet, a discrete-state PINN with built-in aging adaptation for battery modeling, to predict terminal voltage during the discharge process. SeqBattNet consists of two components: (i) an encoder, implemented as the proposed HRM-GRU deep learning module, which generates cycle-specific aging adaptation parameters; and (ii) a decoder, based on the equivalent circuit model (ECM) combined with deep learning, which uses these parameters together with the input current to predict voltage. The model requires only three basic battery parameters and, when trained on data from a single cell, still achieves robust performance. Extensive evaluations across three benchmark datasets (TRI, RT-Batt, and NASA) demonstrate that SeqBattNet significantly outperforms classical sequence models and PINN baselines, achieving consistently lower RMSE while maintaining computational efficiency.