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Again we call the generating function for the sequence \(A\text{.}\) Using differencing:
\begin{align*}
A \amp = 1 + 4x + 9x^2 + 16x^3 + \cdots\\
\underline{-\qquad xA} \amp \underline{\,\, = 0 + x + 4x^2 + 9x^3 + 16x^4 + \cdots}\\
(1-x)A \amp = 1 + 3x + 5x^2 + 7x^3 + \cdots
\end{align*}
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