The centro-polyhedral group \(\langle l,m,n\rangle\), for \(l, m, n \in \mathbb{Z}\), is defined by the presentation
\[\langle x, y, z : x^l = y^m = z^n = xyz \rangle.\]
In this paper, we obtain the periods of \(k\)-nacci sequences in centro-polyhedral groups and related groups.
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