Definition:Pyramidal Number

Definition
The pyramidal numbers are integers defined as sums of sequences of polygonal numbers as follows.

Let $P \left({k, n}\right)$ be the $n$th $k$-gonal number.

Then the $n$th $k$gonal-based pyramidal number $Y \left({k, n}\right)$ is defined as:
 * $\displaystyle Y \left({k, n}\right) = \sum_{i=1}^n P \left({k, i}\right)$

The lower-order pyramidal numbers have special names.


 * Tetrahedral numbers
 * Square-based pyramidal numbers

and so on.