I use the following code
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\begin{equation}
p(m,n):=
\begin{cases}
\displaystyle\frac{2}{9},&\mathrm{mod}(m,3)=0 \\
\displaystyle\frac{1}{9},&\text{otherwise}
\end{cases}\quad\text{for}\ (m,n)\in\mathbb{Z}_{0}^{2}.\notag
\end{equation}

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\renewcommand{\arraystretch}{1.5}
Thanks.