论文标题
Somos上的猜想$ 4 $，$ 6 $和$ 8 $的序列使用Riordan Arrays和Catalan号码
Conjectures on Somos $4$, $6$ and $8$ sequences using Riordan arrays and the Catalan numbers
论文作者
论文摘要
我们对整数序列家庭的形式进行了猜想，其汉克尔转换分别为$（α，β）$ somos $ 4 $序列，$（α，0，γ）$ 6 $ somos $ 6 $序列和$（α，β，β，γ，γ，δ）$ 8 $ $ 8 $ $ $ $α$，$β，$β，$ 8 $ 8 $，涉及的序列可以用某些拉伸的Riordan阵列在加泰罗尼亚数字上的应用，并伴随着（序列）Hankel变换。基于计数自动机方法，Riordan阵列和加泰罗尼亚数字的组合是由某些广义雅各比的研究持续的部分。
We give conjectures on the form of families of integer sequences whose Hankel transforms are, respectively, $(α, β)$ Somos $4$ sequences, $(α, 0, γ)$ Somos $6$ sequences, and $(α, β, γ, δ)$ Somos $8$ sequences, for particular values of $α$, $β$, $γ$, $δ$ which we describe. The sequences involved can be described in terms of the application of certain stretched Riordan arrays to the Catalan numbers, accompanied by a (sequence) Hankel transform. The combination of Riordan array and the Catalan numbers results from the study of certain generalized Jacobi continued fractions, based on the Counting Automata Methodology.
