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Zbl 1119.11014
On the periods of 2-step general Fibonacci sequences in dihedral groups.
(English)
[J] Mat. Vesn. 58, No. 1-2, 47-56 (2006). ISSN 0025-5165

A group $D_n$ is called dihedral if $D_n=\langle a,b:a^n=e,\;b^2=e,\;ab=ba^{-1}\rangle$. The $2$-step general Fibonacci sequences in $D_n$ are defined by $x_0=a$, $x_1=b$, $x_i=x_{i-2}^m x_{i-1}^l$ ($i\geq2$) for integers $m$ and $l$. The authors consider the conditions where the $2$-step general Fibonacci sequences in $D_n$ are simply periodic, namely have repetitions of fixed subsequences from the initial element $a$. They also give the period of the sequences in such cases.
[Takao Komatsu (Hirosaki)]
MSC 2000:
*11B39 Special numbers, etc.

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