deletions | additions       diff --git a/section_Describing_the_Generating_Functions__.tex b/section_Describing_the_Generating_Functions__.tex  index c48a626..765e819 100644  --- a/section_Describing_the_Generating_Functions__.tex  +++ b/section_Describing_the_Generating_Functions__.tex 
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\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}  Similarly we may write \begin{equation}  \chi_11(n)=\begin{cases}  1 & n=0,48\\  2 & n=2,4,7,10,14,17,23,25,31,34,38,41,44,46\\  4 & n=3,5,9,11,16,19,22,24,26,29,32,37,39,43,45\\  6 & n=6,8,12,13,15,18,20,28,30,33,35,36,40,42\\  8 & n=27,21\\  10& n=1,47\\  0 & \mathrm{ow.}  \end{cases}  \end{equation}