In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras. Explicit and recurrent formulae for Split Quaternacci sequences are given, as well as generating functions. Also, matrices related to Split Quaternaccis sequences are investigated. Moreover, new identities connecting Horadam sequences with other known sequences are generated. Analogous identities for Horadam quaternions and split Horadam quaternions are proved.

中文翻译：

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关于 Quaternaccis 的拆分四元数等价物，简称 Split Quaternaccis

在本文中，我们介绍了 Quaternacci 序列 (Quaternaccis) 的推广，称为 Split Quaternacci 序列，它是在分裂四元数代数的基础上产生的。给出了 Split Quaternacci 序列的显式和循环公式，以及生成函数。此外，还研究了与 Split Quaternaccis 序列相关的矩阵。此外，生成了将 Horadam 序列与其他已知序列连接起来的新身份。证明了霍拉丹四元数和分裂霍拉丹四元数的类比恒等式。