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The fun does not stop there: if we replace \(x\) in our original generating function by \(x^2\) we get
\begin{equation*}
\frac{1}{1-x^2} = 1 + x^2 + x^4 + x^6\cdots \mbox{ which generates } 1, 0, 1, 0, 1, 0, \ldots\text{.}
\end{equation*}
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