  We study the 2-adic behavior of the number of domino tilings of a 2n-by-2n
square as nvaries. It was previously known that this number was of the form 2^n
f(n)^2, where f(n) is an odd, positive integer. We show that the function f is
uniformly continuous under the 2-adic metric, and thus extends to a function on
all of Z. The extension satisfies the functional equation f(-1-n) = +- f(n),
where +- sign is + if n is congruent to 0 or 3 modulo 4 and - otherwise.
