On the values of permanents of (0, 1) circulant matrices with three ones per row

Starting from previous works concerning permanents of (0, 1)-circulant matrices with three nonzero entries per row, and just using algebraic methods, we find some congruences satisfied by the values of such permanents, along with simple generalizations to circulants with k ones per row (k ∈ N, k ⩾ 3). We also give an alternative proof for known relations of Fibonacci numbers with some of these values of permanents.