Definition:Pentagonal Pyramidal Number
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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
- 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): $55$