4. Lino eats three kinds of vegetables: artichokes, broccoli and cauliflower. He eats one vegetable every day, and never eats cauliflower the day after he eats broccoli. (a) Determine the numbers of sequences of vegetables Lino can eat over 1 day, over 2 days, and over 3 days. (b) If n 2, explain why the number of sequences of vegetables that Lino can eat over n days while eating broccoli on the nth day is equal to the total number of sequences of vegetables that Lino can eat over n -1 days. (c) Determine a recursive formula for the number of sequences of vegetables that Lino can eat over n days. (d) Determine the number of sequences of vegetables that Lino can eat over 13 days.