  We investigate a variant of the octahedron recurrence which lives in a
3-dimensional lattice contained in [0,n] x [0,m] x R. Generalizing results of
David Speyer math.CO/0402452, we give an explicit non-recursive formula for the
values of this recurrence in terms of perfect matchings. We then use it to
prove that the octahedron recurrence is periodic of period n+m. This result is
reminiscent of Fomin and Zelevinsky's theorem about the periodicity of
Y-systems.
