Palindromicity conjecture for polar degrees of binary no-three-way interaction models

Let $X_{(2,2,k)}^3$ be the no-three-way interaction model of two binary random variables and a third one with state space $k$. Its polar degrees form a sequence. Palindromicity conjecture. The sequence of polar degrees of $X_{(2,2,k)}^3$ is palindromic. This conjecture is based on computations for $k=2$ and $k=3$, where the polar-degree sequences are palindromic; its validity for general $k$ remains open.