... Aztec diamond of order We are interested in tilings of hexagons with lozenges, which are rhombi with unit sides and angles of 120 and 60 degrees, and tilings of Aztec diamonds with dominoes, ... number of tilings of half of a hexagon or half of a diamond, with dents at given places This is not new: see [7] and [8] Express the number of tilings of the figure as a whole as a sum of squares of ... number of tilings of the upper semi-hexagon is Vk−1 (rj − ri ), 0≤i...