Booktabs and row color

As you may know, there is a problem of white space when you try to color rows with book tabs. I found the above solution.

However, when you use @{} in begin{tabular}{@{}*{6}{>$c<$}@{}}
(in order to suppress the space in the edges) some color remains
on the left and right, and I do not know how to put it off.

Thanks

documentclass[9pt]{extbook}
usepackage[french]{keystroke}
usepackage[utf8]{inputenc}
usepackage{amsmath,amsfonts,amssymb,amsthm}
usepackage[table]{xcolor}

usepackage{array,multicol}

usepackage[T1]{fontenc}
usepackage{lmodern} 
usepackage[francais]{babel}

usepackage{booktabs}



colorlet{tableheadcolor}{gray!25} % Table header colour = 25% gray
newcommand{headcol}{rowcolor{tableheadcolor}} %he
colorlet{tablerowcolor}{gray!10} % Table row separator colour = 10% gray
newcommand{rowcol}{rowcolor{tablerowcolor}} %
    % Command topline consists of a (slightly modified) toprule followed by a heavyrule rule of colour tableheadcolor (hence, 2 separate rules)
newcommand{topline}{arrayrulecolor{black}specialrule{0.1em}{abovetopsep}{0.5pt}%
            arrayrulecolor{tableheadcolor}specialrule{belowrulesep}{0pt}{-3pt}%
            arrayrulecolor{black}
            }
    % Command midline consists of 3 rules (top colour tableheadcolor, middle colour black, bottom colour white)
newcommand{midline}{arrayrulecolor{tableheadcolor}specialrule{aboverulesep}{-1pt}{0pt}%
            arrayrulecolor{black}specialrule{lightrulewidth}{0pt}{0pt}%
            arrayrulecolor{white}specialrule{belowrulesep}{0pt}{-3pt}%
            arrayrulecolor{black}
            }
    % Command rowmidlinecw consists of 3 rules (top colour tablerowcolor, middle colour black, bottom colour white)
newcommand{rowmidlinecw}{arrayrulecolor{tablerowcolor}specialrule{aboverulesep}{0pt}{0pt}%
            arrayrulecolor{black}specialrule{lightrulewidth}{0pt}{0pt}%
            arrayrulecolor{white}specialrule{belowrulesep}{0pt}{0pt}%
         arrayrulecolor{black}}
    % Command rowmidlinewc consists of 3 rules (top colour white, middle colour black, bottom colour tablerowcolor)
newcommand{rowmidlinewc}{arrayrulecolor{white}specialrule{aboverulesep}{0pt}{0pt}%
            arrayrulecolor{black}specialrule{lightrulewidth}{0pt}{0pt}%
            arrayrulecolor{tablerowcolor}specialrule{belowrulesep}{0pt}{0pt}%
            arrayrulecolor{black}}
    % Command rowmidlinew consists of 1 white rule
newcommand{rowmidlinew}{arrayrulecolor{white}specialrule{aboverulesep}{0pt}{0pt}%
            arrayrulecolor{black}}
    % Command rowmidlinec consists of 1 tablerowcolor rule
newcommand{rowmidlinec}{arrayrulecolor{tablerowcolor}specialrule{aboverulesep}{0pt}{0pt}%
            arrayrulecolor{black}}
    % Command bottomline consists of 2 rules (top colour
newcommand{bottomline}{arrayrulecolor{white}specialrule{aboverulesep}{0pt}{-2pt}%
            arrayrulecolor{black}specialrule{heavyrulewidth}{0pt}{belowbottomsep}}%
newcommand{bottomlinec}{arrayrulecolor{tablerowcolor}specialrule{aboverulesep}{0pt}{0pt}%
            arrayrulecolor{black}specialrule{heavyrulewidth}{0pt}{belowbottomsep}}%

begin{document}

renewcommand{arraystretch}{1.3}

begin{tabular}{@{}*{6}{>$c<$}@{}} 
topline headcol
x_i&y_i&Delta[x_{i-1},x_i]&Delta[x_{i-2},x_{i-1},x_i]&Delta[x_{i-3},x_{i-2},x_{i-1},x_i]&Delta[x_{i-4},x_{i-3},x_{i-2},x_{i-1},x_i] midline
x_0&{y_0}&&&& 
rowcol x_1&y_1&{Delta[x_0,x_1]}&&& 
x_2&y_2&Delta[x_1,x_2]&{Delta[x_0,x_1,x_2]}&& 
rowcol x_3&y_3&Delta[x_2,x_3]&Delta[x_1,x_2,x_3]&{Delta[x_0,x_1,x_2,x_3]}& 
x_4&y_4&Delta[x_3,x_4]&Delta[x_2,x_3,x_4]&Delta[x_1,x_2,x_3,x_4]&{Delta[x_0,x_1,x_2,x_3,x_4]} 
rowcol vdots &vdots &vdots &vdots &vdots &vdots  
bottomline
end{tabular}
vspace{1cm}

begin{tabular}{*{6}{>$c<$}} 
topline headcol
x_i&y_i&Delta[x_{i-1},x_i]&Delta[x_{i-2},x_{i-1},x_i]&Delta[x_{i-3},x_{i-2},x_{i-1},x_i]&Delta[x_{i-4},x_{i-3},x_{i-2},x_{i-1},x_i] midline
x_0&{y_0}&&&& 
rowcol x_1&y_1&{Delta[x_0,x_1]}&&& 
x_2&y_2&Delta[x_1,x_2]&{Delta[x_0,x_1,x_2]}&& 
rowcol x_3&y_3&Delta[x_2,x_3]&Delta[x_1,x_2,x_3]&{Delta[x_0,x_1,x_2,x_3]}& 
x_4&y_4&Delta[x_3,x_4]&Delta[x_2,x_3,x_4]&Delta[x_1,x_2,x_3,x_4]&{Delta[x_0,x_1,x_2,x_3,x_4]} 
rowcol vdots &vdots &vdots &vdots &vdots &vdots  
bottomline
end{tabular}
end{document}