\documentclass[a4paper,12pt]{article}
\usepackage{array}
\usepackage{colortbl}
\definecolor{umbra}{rgb}{0.8,0.8,0.5}
\def\zero{\multicolumn{1}{>{\columncolor{white}}c}{0}}
\def\colCell#1#2{\multicolumn{1}{>{\columncolor{#1}}c}{#2}}
\begin{document}

\[
\left[\,
\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}}
    {h_{k,1,0}(n)} & {h_{k,1,1}(n)} & {h_{k,1,2}(n)} & \zero & \zero \\
    {h_{k,2,0}(n)} & {h_{k,2,1}(n)} & {h_{k,2,2}(n)} & \zero & \zero \\
    {h_{k,3,0}(n)} & {h_{k,3,1}(n)} & {h_{k,3,2}(n)} & \zero & \zero \\
    {h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & {h_{k,4,2}(n)} & \zero & \zero \\
    \zero & {h_{k,1,0}(n-1)} & {h_{k,1,1}(n-1)} & {h_{k,1,2}(n-1)} & \zero \\
    \zero & {h_{k,2,0}(n-1)} & {h_{k,2,1}(n-1)} & {h_{k,2,2}(n-1)} & \zero \\
    \zero & {h_{k,3,0}(n-1)} & {h_{k,3,1}(n-1)} & {h_{k,3,2}(n-1)} & \zero \\
    \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & {h_{k,4,1}(n-1)} & {h_{k,4,2}(n-1)} & \zero \\
    \zero & \zero & {h_{k,1,0}(n-2)} & {h_{k,1,1}(n-2)} & {h_{k,1,2}(n-2)}\\
  \rowcolor[gray]{0.75}%
    \zero & \zero & {h_{k,2,0}(n-2)} & {h_{k,2,1}(n-2)} & {h_{k,2,2}(n-2)}\\
    \zero & \zero & {h_{k,3,0}(n-2)} & {h_{k,3,1}(n-2)} & {h_{k,3,2}(n-2)}\\
    \zero & \zero & {h_{k,4,0}(n-2)} & {h_{k,4,1}(n-2)} & {h_{k,4,2}(n-2)}
\end{array} \,\right]_{12\times 5}
\]

\end{document}