Investigating linear RNNs such as Mamba, can be challenging because they are currently not efficiently expressible in PyTorch. We propose the abstraction of linear recurrences to gain intuition for the computational structure of these emerging deep learning architectures. After deriving their parallel algorithm, we gradually build towards a simple template CUDA extension for PyTorch. We hope that making linear recurrences accessible to a wider audience inspires further research on linear-time sequence mixing.