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Lookup table (LUT) has shown its efficacy in low-level vision tasks due to the valuable characteristics of low computational cost and hardware independence. However, recent attempts to address the problem of single image super-resolution (SISR) with lookup tables are highly constrained by the small receptive field size. Besides, their frameworks of single-layer lookup tables limit the extension and generalization capacities of the model. In this paper, we propose a framework of series-parallel lookup tables (SPLUT) to alleviate the above issues and achieve efficient image super-resolution. On the one hand, we cascade multiple lookup tables to enlarge the receptive field of each extracted feature vector. On the other hand, we propose a parallel network which includes two branches of cascaded lookup tables which process different components of the input low-resolution images. By doing so, the two branches collaborate with each other and compensate for the precision loss of discretizing input pixels when establishing lookup tables. Compared to previous lookup table-based methods, our framework has stronger representation abilities with more flexible architectures. Furthermore, we no longer need interpolation methods which introduce redundant computations so that our method can achieve faster inference speed. Extensive experimental results on five popular benchmark datasets show that our method obtains superior SISR performance in a more efficient way. The code is available at https://github.com/zhjy2016/SPLUT.