Assume you have an unlimited amount of red, white, and blue marbles. Let Sn denote the number of ways we can fill bags differently with n marbles such that the bags contain an even number of blue marbles. We denote a bag that contains one red, three white, and two blue marbles by rwwwbb.
a) Determine S1, S2, and S3 by listing all possible bags.
b) Give a recurrence relation for Sn where n > 3. Explain your answer.
c) Compute S5 using your recurrence relation. Include your computations.