A New Family of Somos-like Recurrences

Details A New Family of Somos-like Recurrences A New Family of Somos-like Recurrences

2007-09-17

arxiv.org/abs/0709.2529v2

Electronic Journal of Combinatorics, volume 15(1), #R54, April 2008

Mathematics

Combinatorics

9 pages, section added for publication

Scientific paper

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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