Pyramidal Numbers

Let us use three-sided pyramids
(sometimes called tetrahedrons).
To make the pyramid,
start with a triangular arrangement of tennis balls
for the bottom layer.
Next stack up tennis balls layer at
a time, as at right.

If the base of the pyramid has 5 balls along a side,
how many balls does the entire pyramid have in it?
Let us call this a pyramidal number.

Here is a chart that shows the number of balls in the side of a base,
N,
and the corresponding pyramidal numbers.