A novel nth order difference equation that may be integrable

We derive an nth order difference equation as a dual of a very simple periodic equation, and construct (n + 1)/2 explicit integrals and integrating factors of this equation in terms of multi-sums of products. We also present a generating function for the degrees of its iterates, exhibiting polynomial growth. In conclusion we demonstrate how the equation in question arises as a reduction of a system of lattice equations related to an integrable equation of Levi and Yamilov. These three facts combine to suggest the integrability of the nth order difference equation.