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A conjecture based on Somos-4 sequence and its extension

Xiang-Ke Chang Xing-Biao Hu

Number Theory mathscidoc:1912.43165

Linear Algebra and its Applications, 436, (11), 4285-4295, 2012.6
In two recent papers by Barry (2010) [29] and (2011) [30], it is conjectured that Somos-4 admits a solution expressed in terms of Hankel determinant with its elements satisfying a convolution recursion relation. In this paper, Barrys conjecture on Somos-4 is firstly confirmed. Actually, we present a more generalized result. The proof is mainly based on new findings on properties for so-called BlockHankel determinants. The method can also be used to prove another conjecture proposed by Michael Somos, which has been solved by Guoce Xin.
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@inproceedings{xiang-ke2012a,
  title={A conjecture based on Somos-4 sequence and its extension},
  author={Xiang-Ke Chang, and Xing-Biao Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112702756952725},
  booktitle={Linear Algebra and its Applications},
  volume={436},
  number={11},
  pages={4285-4295},
  year={2012},
}
Xiang-Ke Chang, and Xing-Biao Hu. A conjecture based on Somos-4 sequence and its extension. 2012. Vol. 436. In Linear Algebra and its Applications. pp.4285-4295. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112702756952725.
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