Non-overlapping matrices
  Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the $k$-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational. 
Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani
cs.DM math.CO