How to set alternating colors for QTableView headers

Using Qt 5.7.1 along and stylesheets, how can I make the row header section's background color, follow the same alternating pattern of the row cells?

My stylesheet is:

QTableView {
   alternate-background-color: lightblue;
   background-color: grey;
}

QTableView::item:selected {
   background-color: lightgreen;
}

QTableView QTableCornerButton::section {
   background-color: transparent;
   border: 0px ;
}

QHeaderView {
   background-color: grey;
   alternate-background-color: lightblue;
}

QHeaderView::section {
   background-color: transparent;
   alternate-background-color: lightblue;
}

I've tried to enable it through:

ui->tableWidget3->setAlternatingRowColors(true);
ui->tableWidget3->verticalHeader()->setAlternatingRowColors(true);

Unfortunately, it didn't work.

You can implement this behavior not with qss but with subclassing of QHeaderView. For example:

#include <QHeaderView>

class AlterHeader : public QHeaderView
{
    Q_OBJECT
public:
    explicit AlterHeader(Qt::Orientation orientation, QWidget *parent = nullptr);

protected:
    void paintSection(QPainter *painter, const QRect &rect, int logicalIndex) const;
};

void AlterHeader::paintSection(QPainter *painter, const QRect &rect, int logicalIndex) const
{
    Qt::Alignment align = (Qt::AlignHCenter | Qt::AlignVCenter);
    if (logicalIndex % 2 > 0) {
        painter->fillRect(rect, QColor("lightblue"));
    } else {
        painter->fillRect(rect, QColor("grey"));
    }
    painter->drawText(rect, align, QString::number(logicalIndex));
}

And using:

AlterHeader *header = new AlterHeader(Qt::Vertical, ui->tableWidget);
ui->tableWidget->setVerticalHeader(header);