Square Pyramidal Number

A square pyramidal number counts the number of stacked spheres that can be arranged into a pyramid with a square base, one layer at a time, and belongs to the broader family of figurate numbers studied since antiquity by mathematicians including Archimedes and Fibonacci. Algebraically, the nth square pyramidal number is the sum of the first n perfect squares, and it can also be written as the value of a cubic polynomial in n. Beyond counting cannonballs or oranges stacked in a pyramid, these numbers solve other counting problems, such as the number of squares that can be found within a square grid, and they relate to other figurate numbers: the sum of two consecutive square pyramidal numbers is always an octahedral number. A famous exchange between Walter Raleigh and Thomas Harriot about how to count stacked cannonballs eventually led to the discovery that only two numbers, 1 and 4900, are both square and square pyramidal at once. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/