Отличная учебная задачка для курса статфизики (и не только).

Counting microstates of the p-state paramagnet: https://arxiv.org/abs/2108.10340
Steuard Jensen
One effective approach to introducing entropy and the second law is to study models with easily countable states at fixed energy. But such systems are rare: the only familiar examples are the Einstein solid and the two-state paramagnet, which limits the available questions for assignment or discussion. This work considers the more general case of the p-state paramagnet and describes the modestly more complicated counting of its microstates. By computing multiplicities in advance, an instructor can draw on these systems to assign a variety of new problems or open-ended projects that students can complete with the help of a spreadsheet program or analytic calculation.
Comments: 10 pages, 4 figures. Submitted to the American Journal of Physics