The effective Linek conjecture for independent sets of trees

Let $i(T)$ denote the number of independent sets of a tree $T$. Effective Linek's Problem. Every integer greater than $88013$ appears as $i(T)$ for some tree $T$. This is an effective strengthening of Linek's problem, which asks whether infinitely many positive integers fail to occur as the number of independent sets of a tree. The authors report computational verification through $30$ million, but the asserted eventual realization remains open; it contrasts with a conjecture of Han et al. that infinitely many positive integers are not realized by trees.