This question is about arrangements of buttons, which can be red, green or blue, in a line. Let un be the number of distinct lines of n buttons which contain no two consecutive blue buttons. (i) Explain why u1 = 3 and u2 = 8. [4] (ii) Explain why any line of n buttons which contain no two consecutive blue buttons must be one of the two forms below. OOOO OOO n - 2 buttons with no two a red a blue consecutive blue buttons or a button green button OOOO OOO n - 1 buttons with no two a red consecutive blue buttons or a green button [4] (iii) Find un in terms of n. [7]