A New Family of Somos-like Recurrences

@article{Heideman2007ANF,
  title={A New Family of Somos-like Recurrences},
  author={Paul Heideman and Emilie Hogan},
  journal={Electr. J. Comb.},
  year={2007},
  volume={15}
}
We exhibit a three parameter infinite family of quadratic recurrence relations inspired by the well known Somos sequences. For one infinite subfamily we prove that the recurrence generates an infinite sequence of integers by showing that the same sequence is generated by a linear recurrence (with suitable initial conditions). We also give conjectured relations among the three parameters so that the quadratic recurrences generate sequences of integers. 

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