  The connection between matrix integrals and links is used to define matrix
models which count alternating tangles in which each closed loop is weighted
with a factor n, i.e. may be regarded as decorated with n possible colors. For
n=2, the corresponding matrix integral is that recently solved in the study of
the random lattice six-vertex model. The generating function of alternating
2-color tangles is provided in terms of elliptic functions, expanded to 16-th
order (16 crossings) and its asymptotic behavior is given.
