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 $(α, β)$ Somos $4$ sequences. This allows us to prove 4 conjectures of Barry on $(α, β)$ Somos $4$ sequences in a unified way.
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