Let $m,n$ be nonnegative integers.


The sequence $\{a\_{m,n}\}$ satisfies the following three conditions.


1. For any $m$, $a\_{m,0}=a\_{m,1}=1$
2. For any $n$, $a\_{0,n}=1$
3. For any $m\ge0, n\ge1$, $a\_{m+1,n+1}a\_{m,n-1}=a\_{m+1,n-1}a\_{m,n+1}+a\_{m+1,n}a\_{m,n}$


Prove that $a\_{m,n}$ is an integer for any $m\ge0, n\ge0$.


I don't have any good idea. I need your help.



Proving that every term of the sequence is an integer
This is the knight recurrence (Example 4.1) in Fomin and Zelevinsky's paper on the [Laurent phenomenon](http://arxiv.org/abs/math/0104241). They show more generally that if you replace the boundary entries with indeterminates, then all matrix entries are Laurent polynomials.


