Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalised Fibonacci sequences constructed from balancing words   We study growth rates of generalised Fibonacci sequences of a particular
structure. These sequences are constructed from choosing two real numbers for
the first two terms and always having the next term be either the sum or the
difference of the two preceding terms where the pluses and minuses follow a
certain pattern. In 2012, McLellan proved that if the pluses and minuses follow
a periodic pattern and $G_n$ is the $n$th term of the resulting generalised
Fibonacci sequence, then \begin{equation*} \lim_{n\rightarrow\infty}|G_n|^{1/n}
\end{equation*} exists. We extend her results to recurrences of the form
$G_{m+2} = \alpha_m G_{m+1} \pm G_{m}$ if the choices of pluses and minuses,
and of the $\alpha_m$ follow a balancing word type pattern.

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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga