Definition:Pyramidal Number
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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.