Far Eastern Mathematical Journal

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On the Laurent property of the Somos-8 sequences


Bogoutdinova Yu.G.

2019, issue 1, Ñ. 6-9


Abstract
Zelevinsky and Fomin (2002) proved the Laurent property of the Somos-4, 5, 6, 7 sequences. In the paper the smallest number such that the corresponding element of the Somos-8 sequence is not a Laurent polynomial is calculated.

Keywords:
nonlinear recurrent sequences, quadratic sequences, Somos sequences

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References

[1] S. Fomin, A. Zelevinsky, “The Laurent phenomenon”, Adv. Appl. Math., 28, (2002), 119–144.
[2] M. Somos, “Problem 1470”, Crux Mathematicorum, 15, (1989), 208.
[3] D. Gale, “The strange and surprising saga of the Somos sequences”, Math. Intelligencer, 13, (1991), 40–42.
[4] J. L. Malouf, “An integer sequence from a rational recursion”, Discrete Mathematics, 110, (1992), 257–261.
[5] J. Propp, “The Somos Sequence Site”, http://jamespropp.org/somos.html.

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