Pentagonal pyramidal number: Difference between revisions
Appearance
Content deleted Content added
No edit summary |
No edit summary |
||
Line 3: | Line 3: | ||
The first few pentagonal pyramidal numbers are: |
The first few pentagonal pyramidal numbers are: |
||
:[[1 (number)|1]], [[6 (number)|6]], [[18 (number)|18]], [[40 (number)|40]], [[75 (number)|75]], [[126 (number)|126]], [[196 (number)|196]], 288, 405, 550, 726, 936, 1183, 1470, 1800, 2176, 2601, 3078, 3610, 4200, 4851, 5566, 6348, 7200, 8125, 9126 {{OEIS|id=A002411}}. |
:[[1 (number)|1]], [[6 (number)|6]], [[18 (number)|18]], [[40 (number)|40]], [[75 (number)|75]], [[126 (number)|126]], [[196 (number)|196]], [[196 (number)|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 {{mvar|n}}th pentagonal pyramidal number is<ref name=OEIS>[[oeis:A002411]]</ref> |
The formula for the {{mvar|n}}th pentagonal pyramidal number is<ref name=OEIS>[[oeis:A002411]]</ref> |
Revision as of 13:59, 9 November 2020
A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base.[1] The nth 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 (sequence A002411 in the OEIS).
The formula for the nth pentagonal pyramidal number is[2]
so the nth pentagonal pyramidal number is the average of n2 and n3.[2] The nth pentagonal pyramidal number is also n times the nth triangular number.
The generating function for the pentagonal pyramidal numbers is[1]