论文标题
通过$ 2 $确定的算术算术
Arithmetic of Some Sequences Via $2$-determinants
论文作者
论文摘要
我们扩展了对$ 2 $确定的人的调查，这是我们在上一篇论文中定义的。对于第二阶的线性同质复发，我们考虑了满足第二阶线性同质复发的不同序列之间的关系。在证明了D'Ocagne的广义认同之后，我们从单个身份中得出了许多经典身份（及其概括），例如D'Ocagne's，Cassini's，Catalan's和Vajda。一路上，我们研究的序列指定了对有限字母的限制单词的相应组合解释。
We extend our investigation of $2$-determinants, which we defined in a previous paper. For a linear homogenous recurrence of the second order, we consider relations between different sequences satisfying the same linear homogeneous recurrence of the second order. After we prove a generalized identity of d'Ocagne, we derive, from a single identity, a number of classical identities (and their generalizations) such as d'Ocagne's, Cassini's, Catalan's and Vajda's. Along the way, the corresponding combinatorial interpretations in terms of restricted words over a finite alphabet are stated for the sequences we investigate.
