Endergonic reaction

A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. The term is most often used to refer to square pyramidal numbers, which have a square base with 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)

as well as to pyramids with higher numbers of sides

The formula for a r-gonal pyramid number is:

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

r ∈ ℕ, r ≥ 3

This formula factors to:

$\begin{array}{rl}{P}_n^r& =\frac{n(n+1)[n(r-2)-(r-5)]}{(2)(3)}\\ & =\left(\frac{n(n+1)}{2}\right)\left(\frac{n(r-2)-(r-5)}{3}\right)\\ & =T_n\left(\frac{n(r-2)-(r-5)}{3}\right)\\ \end{array}$