Abstract In this paper, we define the Pell-Pell p-sequence and then we discuss the connection of the Pell-Pell p-sequence with Pell and Pell p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Pell-Pell p-numbers by the aid of the nth power of the generating matrix the Pell-Pell p-sequence. Furthermore, we obtain an exponential representation of the Pell-Pell p-numbers and we develop relationships between the Pell-Pell p-numbers and their permanent, determinant and sums of certain matrices.

中文翻译：

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Pell p 数性质的矩阵操作及其推广

摘要 在本文中，我们定义了Pell-Pell p-sequence，然后讨论了Pell-Pell p-sequence与Pell和Pell p-sequences的联系。此外，我们借助生成矩阵 Pell-Pell p 序列的 n 次幂，提供了新的 Binet 公式和 Pell-Pell p 数的新组合表示。此外，我们获得了 Pell-Pell p 数的指数表示，并且我们开发了 Pell-Pell p 数与其永久、行列式和某些矩阵的总和之间的关系。