  Di Francesco introduced Aztec triangles as combinatorial objects for which
their domino tilings are equinumerous with certain sets of configurations of
the twenty-vertex model that are the main focus of his article. We generalize
Di Francesco's construction of Aztec triangles. While we do not know whether
there is again a correspondence with configurations in the twenty-vertex model,
we prove closed-form product formulas for the number of domino tilings of our
generalized Aztec triangles. As a special case, we obtain a proof of Di
Francesco's conjectured formula for the number of domino tilings of his Aztec
triangles, and thus for the number of the corresponding configurations in the
twenty-vertex model.
