Pentagonal pyramidal number
A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base. The th pentagonal pyramidal number is equal to the sum of the first pentagonal numbers.
The first few pentagonal pyramidal numbers are:
The formula for the th pentagonal pyramidal number is
so the th pentagonal pyramidal number is the average of and. The th pentagonal pyramidal number is also times the th triangular number.
The generating function for the pentagonal pyramidal numbers is
