Non-D-finiteness conjecture for Models 5–16

Let $G(t;a,b)$ denote the generating function for the corresponding model, with parameters $t$, $a$, and $b$. A formal power series is D-finite if it satisfies a linear differential equation with polynomial coefficients. Non-D-finiteness conjecture. The generating functions $G(t;a,b)$ for Models 5--16 are not D-finite except when $b=1$.

D-finite solutions have been found for models with symmetry across a vertical line when $b=1$, but solutions have not been found or guessed for other values of $a$ and $b$.