Count 'em Slopes (Count 'em All 17!)

Discrete Mathematics Level 5

A slope grid is a grid that is made by diagonally slicing a regular grid in half, for example, the figure below shows 4 slope grids with dimensions \(1\times1\), \(2\times 2\), \(3\times3\), \(4\times4\) respectively.

Count the total number of quadrilaterals in a \(30\times30\) slope 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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