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Benedict Irwin added section_Describing_the_Generating_Functions__.tex
about 8 years ago
Commit id: 472e23f257d3eb98a3cc1a913b65d03c31ac1d2c
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\section{Describing the Generating Functions more compactly}
We may define a function \begin{equation}
\chi_7(n)=\begin{cases}
1 & n=0,8\\
2 & n=3,5\\
4 & n=2,4,6\\
6 & n=1,7\\
0 & \mathrm{ow.}
\end{cases}
\end{equation}
This allows us to write \begin{equation}
G_7(z) = \frac{z}{(z-1)^2}\frac{\sum_{k=0}^8 \chi_7(k)z^k}{(1+z)(1+z^2)(1+z^4)}
\end{equation}
