Far Eastern Mathematical Journal

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On subsequences of even elements of Somos-6 sequenses


Avdeeva M.O., Bykovskii V.A.

2019, issue 1, Ñ. 3-5


Abstract
It is known that the subsequences of Somos-4 and Somos-5 sequences are Somos-4 sequences. In the paper, it is proved that this property is broken for Somos-6 sequences.

Keywords:
nonlinear recurrent sequences, quadratic sequences, Somos sequences

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References

[1] A. Hone, “Elliptic curves and quadratic recurrence sequences”, Bull. Lond. Math. Soc., v. 37, London Mathematical Society, London, 2005, 161–171.
[2] M. O. Avdeeva, V. A. Bykovskii, “Giperellipticheskie sistemy posledovatel'nostei i funktsii”, Dal'nevostochnyi matematicheskii zhurnal, 16:2, (2016), 115–122.
[3] A. Hone, “Sigma function solution of the initial value problem for Somos 5 sequences”, Trans. Am. Math. Soc., 359:10, (2007), 5019–5034.

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