Attribute-aware sequential recommendation entails predicting the next item a user will interact with based on a chronologically ordered history of past interactions, enriched with item attributes. Existing methods typically leverage self-attention mechanisms to aggregate the entire sequence into a unified representation used for next-item prediction. While effective, these models often suffer from high computational complexity and memory consumption, limiting their ability to process long user histories. This constraint restricts the model's capacity to fully capture long-term user preferences. In some scenarios, modeling item interactions purely through attention may also not be the most effective approach to extract sequential patterns. In this work, we propose ConvRec, an alternative method with linear computational and memory complexity that employs convolutional layers in a hierarchical, down-scaled fashion to generate compact, yet expressive sequence representations. To further enhance the model's ability to capture diverse sequential patterns, each layer aggregates the neighboring items gradually to reach a comprehensive sequence representation. Extensive experiments on four real-world datasets demonstrate that our approach outperforms state-of-the-art sequential recommendation models, highlighting the potential of convolution-based architectures for efficient and effective sequence modeling in recommendation systems. Our implementation code and datasets are available here https://github.com/ismll-research/ConvRec.