On the number of different permanents of some sparse (0,1)-circulant matrices

Starting from known results about the number of possible values for the permanents of (0,1)-circulant matrices with three nonzero entries per row, and whose dimension n is prime, we prove corresponding results for n power of a prime, n product of two distinct primes, and n=2•3h. Supported by some experimental results, we also conjecture that the number of different permanents of n×n (0,1)-circulant matrices with k nonzero per row is asymptotically equal to nk−2/k!+O(nk−3).