  We generalize Aztec diamond theorem (N. Elkies, G. Kuperberg, M. Larsen, and
J. Propp, Alternating-sign matrices and domino tilings, Journal Algebraic
Combinatoric, 1992) by showing that the numbers of tilings of a certain family
of regions in the square lattice with southwest-to-northeast diagonals drawn in
are given by powers of 2. We present a proof for the generalization by using a
bijection between domino tilings and non-intersecting lattice paths.
