The number of functions $f:\{1,2,3,4\} \rightarrow\{a \in \mathbb{Z}:|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f(n+1)=1, \forall n \in\{1,2,3\}$ is

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The number of functions \(f:\{1,2,3,4\} \rightarrow\{a \in \mathbb{Z}:|a| \leq 8\}\) satisfying \(f(n)+\frac{1}{n} f(n+1…