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 (4 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:

$X= \frac{n^2}{2} + n^3\left(\frac{r}{6}-\frac{1}{3}\right) - n\left(\frac{r-5}{6}\right)$