deletions | additions       diff --git a/untitled.tex b/untitled.tex  index dbe4881..fcd5b11 100644  --- a/untitled.tex  +++ b/untitled.tex 
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we can see the subsequence $71,213,19170,19170,1811565$ is $1,3,270,270,25515$ when divided by $71$.  The number of $3$'s in the lead coeficcient are $1,3,3,5,6,8$ which could be a number of sequences.  The number of $3$'s in the second coefficients are $0,1,3,3,6$ which could also be many sequences. Then we have  \begin{equation}  \pi_m(k) = \sum_{i=0}^{m-1}\frac{\left[\prod_{j=0}^{i} (m-j)\right]}{d_{i+1}}\sigma_i(m)k^{m-i}  \end{equation}  and we focus on the $\sigma_i(m)$ polynomials \begin{equation}  \simga_0(m)=3 \\  \sigma_1(m)=27m+71 \\  \sigma_2(m)=27m^2+213m-528\\  \sigma_3(m)=1215m^3+19170 m^2-69835 m+191522\\  \sigma_4(m)=729m^4+19170m^3-66945m^2+199686 m-1863360\\  \sigma_5(m)=45927 m^5+1811565 m^4-3671325 m^3-20584781 m^2-243156858 m-181415824  \end{equation}