Alkauskas's divisibility conjecture for binary partitions

Let $b_{2}(n)$ denote the number of binary partitions of $n$. Alkauskas's conjecture. For every $h\in\mathbb{N}$ with $8\nmid h$, there exist infinitely many $n$ such that $h$ divides $b_{2}(n)$. The conjecture is presented as an open problem concerning divisibility values of the binary partition sequence.