Variation on 8.4#49] A coding system encodes messages using strings of hexadecimal (base 16) digits. A codeword is considered valid if and only if it contains an even number of 7s. (a) Find a linear nonhomogeneous recurrence relation for the number of valid codewords of length n, including the initial conditions. 10 points Replace this text with your answer. (b) Solve this recurrence relation using Theorem 6 in Section 8.2.[10 points Replace this text with vour answer. (c) Solve this recurrence relation using generating functions. [10 points Replace this text with your