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Fast dose calculation is critical for online and real time adaptive therapy workflows. While modern physics-based dose algorithms must compromise accuracy to achieve low computation times, deep learning models can potentially perform dose prediction tasks with both high fidelity and speed. We present a deep learning algorithm that, exploiting synergies between Transformer and convolutional layers, accurately predicts broad photon beam dose distributions in few milliseconds. The proposed improved Dose Transformer Algorithm (iDoTA) maps arbitrary patient geometries and beam information (in the form of a 3D projected shape resulting from a simple ray tracing calculation) to their corresponding 3D dose distribution. Treating the 3D CT input and dose output volumes as a sequence of 2D slices along the direction of the photon beam, iDoTA solves the dose prediction task as sequence modeling. The proposed model combines a Transformer backbone routing long-range information between all elements in the sequence, with a series of 3D convolutions extracting local features of the data. We train iDoTA on a dataset of 1700 beam dose distributions, using 11 clinical volumetric modulated arc therapy (VMAT) plans (from prostate, lung and head and neck cancer patients with 194-354 beams per plan) to assess its accuracy and speed. iDoTA predicts individual photon beams in ~50 milliseconds with a high gamma pass rate of 97.72% (2 mm, 2%). Furthermore, estimating full VMAT dose distributions in 6-12 seconds, iDoTA achieves state-of-the-art performance with a 99.51% (2 mm, 2%) pass rate. Offering the sub-second speed needed in online and real-time adaptive treatments, iDoTA represents a new state of the art in data-driven photon dose calculation. The proposed model can massively speed-up current photon workflows, reducing calculation times from few minutes to just a few seconds.