Pentagonal Pyramidal Number - GeeksforGeeks

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++
Java
Python3
C#
PHP
Javascript
// CPP Program to get nth Pentagonal// pyramidal number.#include <bits/stdc++.h>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 Programint main(){    int n = 4;    cout << pentagon_pyramidal(n) << endl;    return 0;}
// 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 Codepublic static void main (String[] args){    int n = 4;    System.out.println(pentagon_pyramidal(n));}} // This code is contributed by anuj_67.
# 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 Programn = 4print(int(pentagon_pyramidal(n)))
// 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 Codestatic public void Main (){    int n = 4;    Console.WriteLine(pentagon_pyramidal(n));}} // This code is contributed by ajit.
<?php// PHP Program to get nth// Pentagonal pyramidal number. // function to get nth// Pentagonal pyramidal number.function pentagon_pyramidal($n){    $sum = 0;     // Running loop from 1 to n    for ($i = 1; $i <= $n; $i++)    {         // get nth pentagonal number        $p = (3 * $i *                  $i - $i) / 2;         // add to sum        $sum = $sum + $p;    }    return $sum;} // Driver Code$n = 4;echo pentagon_pyramidal($n); // This code is contributed by m_kit?>
<script>// javascript Program to get nth// Pentagonal pyramidal number. // function to get nth// Pentagonal pyramidal number.function pentagon_pyramidal(n){    var sum = 0;     // Running loop from 1 to n    for (i = 1; i <= n; i++)    {         // get nth pentagonal number        var p = (3 * i * i - i) / 2;         // add to sum        sum = sum + p;    }    return sum;} // Driver Codevar n = 4;document.write(pentagon_pyramidal(n)); // This code is contributed by Amit Katiyar</script>
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++
Java
Python3
C#
PHP
Javascript
// CPP Program to get nth Pentagonal// pyramidal number.#include <bits/stdc++.h>using namespace std; // function to get nth Pentagonal// pyramidal number.int pentagon_pyramidal(int n){    return n * n * (n + 1) / 2;} // Driver Programint main(){    int n = 4;    cout << pentagon_pyramidal(n) << endl;    return 0;}
// 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 Codepublic static void main (String[] args){    int n = 4;    System.out.println(pentagon_pyramidal(n));}} // This code is contributed by ajit
# 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 Programn = 4print(int(pentagon_pyramidal(n)))
// 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 Codestatic public void Main (){    int n = 4;    Console.WriteLine(            pentagon_pyramidal(n));}} // This code is contributed// by ajit
<?php// PHP Program to get// nth Pentagonal// pyramidal number. // function to get// nth Pentagonal// pyramidal number. function pentagon_pyramidal($n){    return $n * $n *          ($n + 1) / 2;} // Driver Code$n = 4;echo pentagon_pyramidal($n);     // This code is contributed// by akt_mit?>
<script>// javascript Program to get nth// Pentagonal pyramidal number.      // function to get nth// Pentagonal pyramidal number.function pentagon_pyramidal(n){    return n * n *          (n + 1) / 2;} // Driver Codevar n = 4;document.write(pentagon_pyramidal(n)); // This code is contributed by Princi Singh</script>
Output :  
40
 
Time Complexity : O(1)  
 
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