Pyramidal number

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

as well as to pyramids with higher numbers of sides

The formula for an r-gonal pyramidal number is:

with r ∈ ℕ, r ≥ 3.

This formula can be factorized as follows:

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