G-sets and linear recurrences modulo primes

Let p be a prime number with p≠2. We consider second order linear recurrence relations of the form S_n=aS_n-1+bS_n-2 over the finite field Z_p (we assume b≠0). Results regarding the period and distribution of elements in the sequence {S₀, S₁,...} are well-known (see works by Kuipers, Niederreiter, Wall, and Webb). We examine these second order recurrences using matrices, groups, and G-sets.