Height growth of solutions and a discrete Painlevé equation

A Al-Ghassani, R Halburd

Consider the discrete equation $$y_{n+1}+y_{n-1}=\frac{a_n+b_n{y}_n+c_n{y}_n^2}{1-y_n^2},$$ where the right side is of degree two in $y_n$ and where the coefficients $a_n$, $b_n$ and…