Color sequences, ordered sets of colors for data visualization, that balance aesthetics with accessibility considerations are presented. In order to model aesthetic preference, data were collected with an online survey, and the results were used to train a machine-learning model. To ensure accessibility, this model was combined with minimum-perceptual-distance constraints, including for simulated color-vision deficiencies, as well as with minimum-lightness-distance constraints for grayscale printing, maximum-lightness constraints for maintaining contrast with a white background, and scores from a color-saliency model for ease of use of the colors in verbal and written descriptions. Optimal color sequences containing six, eight, and ten colors were generated using the data-driven aesthetic-preference model and accessibility constraints. Due to the balance of aesthetics and accessibility considerations, the resulting color sequences can serve as reasonable defaults in data-plotting codes, e.g., for use in scatter plots and line plots.