Definition:Pyramidal Number

From ProofWiki
Jump to navigation Jump to search

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:

and so on.

  • Results about pyramidal numbers can be found here.