Definition:Pyramidal Number

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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.