Ben has a collection of 14 stuffed animals (Alvin the Chipmunk, Belle the Bobcat, Craig the Crab, etc. down to Newt the Newt. He keeps them in alphabetical order in a long line on his shelf. One day after taking them down to play with for a while Ben decides to put them back and he wonders how many ways he could put them back if each animal needed to be back in its original position or directly to the left or right of its original position. So, for example, Belle could either stay in the second place or be in Alvin or Craig's place in the new arrangement. How many different ways can Ben put the animals back on the shelf under this scheme?
