Determinants and inverses of r-circulant matrices associated with a number sequence

Let W-n = circ(r) (W-1, W-2, ... , W-n) be the r -circulant matrix associated with the numbers defined by the recursive relation W-n = pW(n-1) + qW(n-2) with initial conditions W-0 = a and W-1 = b, where a, b, p, q is an element of Z and n >= 2. We obtain some formulas for the determinants and inverses of Wn. Some bounds for spectral norms of W-n are obtained as applications.