Categorification of the Fibonacci numbers using representations of   quivers
  In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the 3-regular star. Now we deal in a similar way with the odd-index Fibonacci numbers. The Fibonacci modules introduced here provide a convenient categorification of the Fibonacci numbers. 
Philipp Fahr and Claus Michael Ringel
math.RT math.CO