Pyramidal number

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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 [1]

The formula for an r-gonal pyramidal number is:

with r ∈ , r ≥ 3.

This formula can be factorized as follows:


  1. ^ Sloane, N. J. A. (ed.). "Sequence A002414". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.