Write a matlab code without build in functions

Design a MATLAB code to construct a natural cubic spline P(x) that passes though the points (1, 1), (4, 1/4), (7, 1/7), (10, 1/10), (13, 1/13) and (16, 1/16). (a) Use the constructed cubic spline to interpolate x = 3; (b) Find the error e_1 = |1/3 - P(3)|