Periodic sequences, binomials modulo a prime power, and a math/music application

We study, through new recurrence relations for certain binomial coefficients modulo a power of a prime, the evolution of the iterated anti-differences of periodic sequences modulo m. We prove that one can reduce to study iterated antidifferences of constant sequences. Finally we apply our results to describe the dynamics of the iterated applications of the Vieru operator to the sequence considered by the Romanian composer Vieru in his Book of Modes [20].