What Squares Are in the Square Grid?

squares

rectangles

n

1

2

3

4

5

Given a square grid of size

n×n

, this Demonstration shows each of its grid subsquares or grid subrectangles. The formula enumerating subsquares is

n(n+1)(2n+1)/6

. The formula enumerating subrectangles is

2

(n(n+1)/2)

.