Enumeration of Domino Tilings of an Aztec Rectangle with boundary   defects
  Helfgott and Gessel gave the number of domino tilings of an Aztec Rectangle with defects of size one on the boundary of one side. In this paper we extend this to the case of domino tilings of an Aztec Rectangle with defects on all boundary sides. 
Manjil P. Saikia
math.CO