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# Pentagonal Pyramidal Number

• Last Updated : 12 Apr, 2021

Given a number n, find the nth pentagonal pyramidal number.
A Pentagonal Pyramidal Number belongs to the figurate number class. It is the number of objects in a pyramid with a pentagonal base. The nth pentagonal pyramidal number is equal to sum of first n pentagonal numbers
Examples:

```Input : n = 3
Output : 18

Input : n = 7
Output : 196```

Method 1: (Naive Approach) :
This approach is simple. It says to add all the pentagonal numbers up to n (by running loop) to get nth Pentagonal pyramidal number.

Below is the implementation of this approach:

## C++

 `// CPP Program to get nth Pentagonal``// pyramidal number.``#include ``using` `namespace` `std;` `// function to get nth Pentagonal``// pyramidal number.``int` `pentagon_pyramidal(``int` `n)``{``    ``int` `sum = 0;` `    ``// Running loop from 1 to n``    ``for` `(``int` `i = 1; i <= n; i++) {` `        ``// get nth pentagonal number``        ``int` `p = (3 * i * i - i) / 2;` `        ``// add to sum``        ``sum = sum + p;``    ``}``    ``return` `sum;``}` `// Driver Program``int` `main()``{``    ``int` `n = 4;``    ``cout << pentagon_pyramidal(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to get nth``// Pentagonal pyramidal number.``import` `java.io.*;` `class` `GFG``{` `// function to get nth``// Pentagonal pyramidal number.``static` `int` `pentagon_pyramidal(``int` `n)``{``    ``int` `sum = ``0``;` `    ``// Running loop from 1 to n``    ``for` `(``int` `i = ``1``; i <= n; i++)``    ``{` `        ``// get nth pentagonal number``        ``int` `p = (``3` `* i * i - i) / ``2``;` `        ``// add to sum``        ``sum = sum + p;``    ``}``    ``return` `sum;``}` `// Driver Code``public` `static` `void` `main (String[] args)``{``    ``int` `n = ``4``;``    ``System.out.println(pentagon_pyramidal(n));``}``}` `// This code is contributed by anuj_67.`

## Python3

 `# Python3 Program to get nth Pentagonal``# pyramidal number.``  ` `# function to get nth Pentagonal``# pyramidal number.``def` `pentagon_pyramidal(n):``    ``sum` `=` `0` `    ``# Running loop from 1 to n``    ``for` `i ``in` `range``(``1``, n ``+` `1``):``  ` `        ``# get nth pentagonal number``        ``p ``=` `( ``3` `*` `i ``*` `i ``-` `i ) ``/` `2` `        ``# add to sum``        ``sum` `=` `sum` `+` `p      `` ` `    ``return` `sum` `  ` `# Driver Program``n ``=` `4``print``(``int``(pentagon_pyramidal(n)))`

## C#

 `// C# Program to get nth``// Pentagonal pyramidal number.``using` `System;` `class` `GFG``{``    ` `// function to get nth``// Pentagonal pyramidal number.``static` `int` `pentagon_pyramidal(``int` `n)``{``    ``int` `sum = 0;` `    ``// Running loop from 1 to n``    ``for` `(``int` `i = 1; i <= n; i++)``    ``{` `        ``// get nth pentagonal number``        ``int` `p = (3 * i *``                 ``i - i) / 2;` `        ``// add to sum``        ``sum = sum + p;``    ``}``    ``return` `sum;``}` `// Driver Code``static` `public` `void` `Main ()``{``    ``int` `n = 4;``    ``Console.WriteLine(pentagon_pyramidal(n));``}``}` `// This code is contributed by ajit.`

## PHP

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## Javascript

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Output :

`40`

Time Complexity : O(n)

Method 2: (Efficient Approach) :
In this approach, we use formula to get nth Pentagonal pyramidal number in O(1) time.

nth Pentagonal pyramidal number = n2 (n + 1) / 2
Below is the implementation of this approach:

## C++

 `// CPP Program to get nth Pentagonal``// pyramidal number.``#include ``using` `namespace` `std;` `// function to get nth Pentagonal``// pyramidal number.``int` `pentagon_pyramidal(``int` `n)``{``    ``return` `n * n * (n + 1) / 2;``}` `// Driver Program``int` `main()``{``    ``int` `n = 4;``    ``cout << pentagon_pyramidal(n) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to get nth``// Pentagonal pyramidal number.``import` `java.io.*;` `class` `GFG``{``    ` `// function to get nth``// Pentagonal pyramidal number.``static` `int` `pentagon_pyramidal(``int` `n)``{``    ``return` `n * n *``          ``(n + ``1``) / ``2``;``}` `// Driver Code``public` `static` `void` `main (String[] args)``{``    ``int` `n = ``4``;``    ``System.out.println(pentagon_pyramidal(n));``}``}` `// This code is contributed by ajit`

## Python3

 `# Python3 Program to get nth Pentagonal``# pyramidal number.``  ` `# function to get nth Pentagonal``# pyramidal number.``def` `pentagon_pyramidal(n):    ``    ``return` `n ``*` `n ``*` `(n ``+` `1``) ``/` `2` `  ` `# Driver Program``n ``=` `4``print``(``int``(pentagon_pyramidal(n)))`

## C#

 `// C# Program to get nth``// Pentagonal pyramidal number.``using` `System;` `class` `GFG``{``    ` `// function to get nth``// Pentagonal pyramidal number.``static` `int` `pentagon_pyramidal(``int` `n)``{``    ``return` `n * n *``          ``(n + 1) / 2;``}` `// Driver Code``static` `public` `void` `Main ()``{``    ``int` `n = 4;``    ``Console.WriteLine(``            ``pentagon_pyramidal(n));``}``}` `// This code is contributed``// by ajit`

## PHP

 ``

## Javascript

 ``

Output :

`40`

Time Complexity : O(1)

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