Lazily Tying the Knot for 1 Dimensional Dynamic Programming

Several years ago I took an algorithms course where we were giving the following problem (or one like it): There is a building of n floors with an elevator that can only go up 2 floors at a time and down 3 floors at a time. Using dynamic programming write a function that will compute the number of steps it takes the elevator to get from floor i to floor j. This is obviously easy using a stateful a