Definition:Pyramidal Number

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:
 * $$Y \left({k, n}\right) = \sum_{i=1}^n P \left({k, i}\right)$$

The lower-order pyramidal numbers have special names.


 * Tetrahedral numbers;
 * Square-based pyramidal numbers;

and so on.