Since it's a wise idea to have a stopping condition when gambling, a gambler decides to play a game until they lose three times in a row. Let W and L denote wins and losses respectively, and let aN denote the number of arrangements of wins and losses over N games. Here are the possibilities for the arrangements of wins and losses for the first values of aN: age 1 (LLL) a4=1 (WLLL) a5-2 (WWLLL, LWLLL) ag = 4 (WWWLLL, WLWLLL, LWWLLL, LLWLLL) etc... Bearing in mind that any sequence of N games must start with the arrangement W, LW, or LLW, find a recurrence relation that gives a formula for the number of arrangements of wins and losses for aN