Somos-4 and elliptic systems of sequences (Q521398)

The double Somos-4 sequences \(\{ A_n \}\) and \(\{ B_n \}\) with no zero elements and with initial terms \[ A_{\pm 2}, A_{\pm 1}, A_{0}, B_{\pm 2}, B_{\pm 1}, B_{0} \] are defined by the recurrence relations: \[ A_{n+2}B_{n-2} = \alpha A_{n+1}B_{n-1} + \beta A_{n}B_{n}, \] \[ A_{n-2}B_{n+2} = \gamma A_{n-1}B_{n+1} + \delta A_{n}B_{n}. \] General formulas for their elements are obtained. A sufficient integrality condition for such sequences is presented.