Pyramidal number

A pyramidal number is a figurate number that represents a pyramid with a base and a given number of sides. The term is most often used to refer to square pyramidal numbers, which have four sides, but it can also refer to:

• Triangular pyramidal number (three sides)
• Square pyramidal number (four sides)
• Pentagonal pyramidal number (five sides)
• Hexagonal pyramidal number (six sides)
• Heptagonal pyramidal number (seven sides)

The formula for a r-gonal pyramid number is:

$X={\frac {3n^{2}+n^{3}(r-2)-n(r-5)}{6}}$

where r is a natural number greater or equal to 3.