In this paper, we introduce the incomplete Horadam numbers W n (k), and hyper-Horadam numbers W (k) n , which generalize the Horadam's numbers defined by the recurrence W n = pW n−1 + qW n−2 , with W 0 = a and W 1 = b. We give some combinatorial properties. As an application, we evaluate a lower and upper bounds for the spectral norms of r-circulant matrices associated with these two generalizations. Moreover, we establish a new bounds for the spectral norms of r-circulant matrices associated with Horadam's numbers in terms of incomplete Horadam and hyper-Horadam numbers.