Let $\{s_n\}$ be the Somos-$4$ sequence, which is defined by $$s_{n+4}s_n=\alpha s_{n+3}s_{n+1}+\beta s_n^2.$$ It is known that $s_n$ is a Laurent polynomial: $s_n\in\mathbb{Z}[s_1^{\pm1}, \ldots, s_4^{\pm1},\alpha, \beta].$ From the article Speyer, D. E. Perfect matchings and the octahedron recurrence we know that $\{s_n\}$ (and Somos-$5$ as well) satisfy the "positivity conjecture": all coefficients in this Laurent polynomial are positive.
Is the "positivity conjecture" known for Somos-$6$-$7$ sequences?
