This study examines the properties of an r-circulant matrix whose entries are defined by the generalized k-Pell-Tribonacci sequence {P_k,n}. Explicit expressions are derived for the Frobenius (Euclidean) norm and the entrywise \ell_1-norm, together with closed-form formulas for the eigenvalues and the determinant of the matrix. Furthermore, upper and lower bounds for the spectral norm are established, yielding results that generalize previously reported ones corresponding to particular sequences while also providing sharper bounds for the considered norms.