Definition:Pentagonal Pyramidal Number

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Pentagonal pyramidal numbers are those denumerating a collection of objects which can be arranged in the form of a pentagonal pyramid.

The $n$th pentagonal pyramidal number $Q_n$ is defined as:

$\displaystyle Q_n = \sum_{k \mathop = 1}^n P_k$

where $P_k$ is the $k$th pentagonal number.


The sequence of pentagonal pyramidal numbers begins as follows:

$0, 1, 6, 18, 40, 75, 126, 196, 288, 405, 550, 726, 936, 1183, \ldots$

Also see

  • Results about pentagonal pyramidal numbers can be found here.