Rectangles in cross-hatched grids

In a $3\times 2$ cross-hatched grid, a total of $37$ different rectangles could be situated within that grid as indicated in the sketch.

There are $5$ grids smaller than $3\times 2$, vertical and horizontal dimensions being important, i.e. $1\times 1$, $2\times 1$, $3\times 1$, $1\times 2$ and $2\times 2$. If each of them is cross-hatched, the following number of different rectangles could be situated within those smaller grids:

size	count
1x1	1
2x1	4
3x1	8
1x2	4
2x2	18

Adding those to the $37$ of the $3\times 2$ grid, a total of $72$ different rectangles could be situated within $3\times 2$ and smaller grids.

How many different rectangles could be situated within $47\times 43$ and smaller grids?