  By using Sulanke-Xin continued fractions method, Xin proposed a recursion
system to solve the Somos 4 Hankel determinant conjecture. We find Xin's
recursion system indeed give a sufficient condition for $(\alpha, \beta)$ Somos
$4$ sequences. This allows us to prove 4 conjectures of Barry on $(\alpha,
\beta)$ Somos $4$ sequences in a unified way.
