Definition:Pentagonal Pyramidal Number

Definition

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:

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

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

Sequence

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

• Closed Form for Pentagonal Pyramidal Numbers

• Definition:Pyramidal Number
• Definition:Tetrahedral Number
• Definition:Square Pyramidal Number

• Results about pentagonal pyramidal numbers can be found here.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $55$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $55$