Pentagonal pyramidal number
- Pentagonal pyramidal number
A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base.[MathWorld|title=Pentagonal Pyramidal Number|urlname=PentagonalPyramidalNumber] The "n"th pentagonal pyramidal number is equal to the sum of the first "n" pentagonal numbers.]The first few pentagonal pyramidal numbers are:
1, 6, 18, 40, 75, 126, 196, 288, 405, 550, 726, 936, 1183, 1470, 1800, 2176, 2601, 3078, 3610, 4200, 4851, 5566, 6348, 7200, 8125, 9126 OEIS|id=A002411
The formula for the "n"th pentagonal pyramidal number is[] ]:
so the "n"th pentagonal pyramidal number is the average of n2 and n3.[ The "n"th pentagonal pyramidal number is also "n" times the "n"th triangular number.]The generating function for the pentagonal pyramidal numbers is:
ee also
*Triangular pyramidal number
*Square pyramidal number
References
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