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.

This is one part of Quadrilatorics.

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