$width = 220;
$height = 100;

difference() {
    linear_extrude(5)
        square([$width, $height]);
    for (i=[0:1:5]) {
        $even_row = i%2;
        translate([0, 10 + i * 16, -5]) row_cylinders(diameter=14, gap=6, x_offset=$even_row*4);            
    }
};

module row_cylinders(diameter=20, gap=10, x_offset=0, length=220) {
    // One spacing will be split between the start and the end.
    $count = floor((length - 2 * x_offset) / (diameter + gap));
    // It's not always possible to perfectly fit all the columns, sometimes
    // you end up with extra space. In that case, the space will be split
    // into the start and the end.    
    $leftover = (length - 2 * x_offset) % (diameter + gap);
    
    for (dx=[(diameter + gap + $leftover) / 2 + x_offset
            : diameter + gap
            : length - ((gap + $leftover) / 2 + x_offset)
            ]) {
        translate([dx, 0, 0]) cylinder(h=20, d=diameter);
    }
}