<DataGrid  AlternationCount="6">
            
            <DataGrid.RowStyle>
                <Style TargetType="DataGridRow">
                    <Style.Triggers>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="0">
                            <Setter Property="Background" Value="LightGray" />
                        </Trigger>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="1">
                            <Setter Property="Background" Value="LightGray" />
                        </Trigger>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="2">
                            <Setter Property="Background" Value="LightGray" />
                        </Trigger>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="3">
                            <Setter Property="Background" Value="White" />
                        </Trigger>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="4">
                            <Setter Property="Background" Value="White" />
                        </Trigger>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="5">
                            <Setter Property="Background" Value="White" />
                        </Trigger>
                    </Style.Triggers>
                </Style>
            </DataGrid.RowStyle>
            ...
</DataGrid>

        private void dg_LoadingRow(object sender, DataGridRowEventArgs e)
        {
            switch ((e.Row.GetIndex() + 6) % 6)
            {
                case 0:
                    e.Row.Background = Brushes.LightGray;
                    break;

                case 1:
                    e.Row.Background = Brushes.LightGray;
                    break;

                case 2:
                    e.Row.Background = Brushes.LightGray;
                    break;

                case 3:
                    e.Row.Background = Brushes.White;
                    break;

                case 4:
                    e.Row.Background = Brushes.White;
                    break;

                case 5:
                    e.Row.Background = Brushes.White;
                    break;

                default:
                    break;
            }
        }