# Direct and Inverse efficient mapping of 3D cartesian positions in a 1D array

I saved a sample of $$N$$ Cartesian locations $$\{x_i, y_j, z_k\}$$ inside a one-dimensional array $$\mathbf{a} = \{a_l\}_{l = 1}^N$$. How can I access back (efficiently) the $$l$$-location of the array $$\mathbf{a}$$ knowing just the three $$i,j,k$$ Cartesian indices?