Is there an effective way of finding a particular $x_n$, say $x_5$, of a system of difference equations $x_{n}=ax_{n+1}+bx_{n-1}$ where $a, b$ are constants and the $n$'s say are $\leq k$ (apart from actually substituting each equation into the next)? Thanks.
System of difference equations
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linear-algebra
recurrence-relations
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