13. Eight $2 \times 1$ small rectangles as shown in the right figure can be used to form a $4 \times 4$ square. If a square formed by these small rectangles is the same as another square after rotation, they are considered the same square. How many different squares, which are symmetrical up and down and have two adjacent blank small squares in the first row, can be formed from all possible square formations?
Because in the square shape, it is symmetrical up and down, and the given shape is asymmetrical up and down (the second and third layers can only be placed horizontally, not vertically), we only need to consider the $2 \times 4$ rectangle of the first and second layers. There are two cases: the two blank squares are in the third and fourth columns (rotating the two blank squares in the first and second columns can result in the two blank squares being in the third and fourth columns) and the two blank squares are in the second and third columns. Therefore, the answer is five.