Definition:Pyramidal Number

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

Let $\map P {k, n}$ be the $n$th $k$-gonal number.

Then the $n$th $k$-gonal-based pyramidal number $\map Y {k, n}$ is defined as:
 * $\ds \map Y {k, n} = \sum_{i \mathop = 1}^n \map P {k, i}$

Also see
The lower-order pyramidal numbers have special names:


 * Definition:Tetrahedral Number
 * Definition:Square Pyramidal Number

and so on.