Count 'em Staircases (Count 'em All 16!)Discrete Mathematics Level 4
A staircase grid is a grid of squares that resembles a staircase shape, for example, the figure below shows 4 staircase grids with dimensions \(1\times1\), \(2\times2\), \(3\times3\), \(4\times4\) respectively.
Count the total number of quadrilaterals in a \(30\times 30\) staircase grid (that is, when \(a=30\)).
Clarification: A quadrilateral is a polygon that has 4 sides.