Pentatope number

Namachila November 19, 2025

0 0 3 minutes read

Given a number n, find the nth Pentatope number. A pentatope number is represented by the fifth number in any row of Pascal’s Triangle. As it is fifth number, it should start from row having at least 5 numbers. So, it starts from row 1 4 6 4 1. The formula for the nth pentatope number is: n (n+1) (n+2) (n+3) / 24
Starting Pentatope numbers are : 1, 5, 15, 35, 70, 126, 210, 330, 495…..
Pentatope Numbers:

In the above figure, red color circled numbers are pentatope numbers.
Examples:

Input: 4
Output: 35

Input: 8
Output: 330

Below is the implementation for nth Pentatope Number :

C++

// CPP Program to find the
// nth Pentatope number
#include <bits/stdc++.h>
using namespace std;
 
// function for Pentatope
// number
int Pentatope_number(int n)
{
    // formula for find Pentatope
    // nth term
    return n * (n + 1) * (n + 2) * (n + 3) / 24;
}
 
// Driver Code
int main()
{
    int n = 7;
    cout << n << "th Pentatope number :"
         << Pentatope_number(n) << endl;
 
    n = 12;
    cout << n << "th Pentatope number :"
         << Pentatope_number(n) << endl;
 
    return 0;
}

Java

// Java Program to find the nth Pentatope
// number
import java.io.*;
 
class GFG {
 
    // function for Pentatope
    // number
    static int Pentatope_number(int n)
    {
         
        // formula for find Pentatope
        // nth term
        return n * (n + 1) * (n + 2) * 
                         (n + 3) / 24;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        int n = 7;
        System.out.println( n + "th "
                   + "Pentatope number :"
                  + Pentatope_number(n));
                   
        n = 12;
        System.out.println( n + "th "
                  + "Pentatope number :"
                 + Pentatope_number(n));
    }
}
 
// This code is contributed by anuj_67.

Python3

# Python3 program to find
# nth Pentatope number
 
# Function to calculate
# Pentatope number
def Pentatope_number(n):
 
    # Formula to calculate nth
    # Pentatope number
    return (n * (n + 1) * (n + 2) 
                 * (n + 3) // 24)
 
# Driver Code
n = 7
print("%sth Pentatope number : " %n,
                    Pentatope_number(n))
n = 12
print("%sth Pentatope number : " %n,
                    Pentatope_number(n))
 
# This code is contributed by ajit.     

C#

// C# Program to find the nth Pentatope 
// number
using System;
 
class GFG {
 
    // function for Pentatope
    // number
    static int Pentatope_number(int n)
    {
         
        // formula for find Pentatope
        // nth term
        return n * (n + 1) * (n + 2) * 
                         (n + 3) / 24;
    }
     
    // Driver Code
    public static void Main ()
    {
        int n = 7;
        Console.WriteLine( n + "th "
                + "Pentatope number :"
               + Pentatope_number(n));
                
        n = 12;
        Console.WriteLine( n + "th "
                + "Pentatope number :"
               + Pentatope_number(n));
    }
}
 
// This code is contributed by anuj_67.

PHP

<?php
// PHP Program to find the
// nth Pentatope number
 
// function for Pentatope
// number
function Pentatope_number($n)
{
     
    // formula for find Pentatope
    // nth term
    return $n * ($n + 1) * 
          ($n + 2) * ($n + 3) 
                       / 24;
}
 
    // Driver Code
    $n = 7;
    echo $n , "th Pentatope number :"
            , Pentatope_number($n), "\n";
 
    $n = 12;
    echo $n , "th Pentatope number :"
            , Pentatope_number($n) ;
             
// This code is contributed by anuj_67.
 
?>

Javascript

<script>
 
// Javascript  Program to find the
// nth Pentatope number
 
// function for Pentatope
// number
function Pentatope_number(n)
{
     
    // formula for find Pentatope
    // nth term
    return n * (n + 1) *(n + 2) * (n + 3)/ 24;
}
 
    // Driver Code
    let n = 7;
    document.write( n + "th "
                   + "Pentatope number : "
                  + Pentatope_number(n)+"<br>") ;
 
     n = 12;
    document.write( n + "th "
                   + "Pentatope number : "
                  + Pentatope_number(n)) ;
             
 
// This code is contributed by sravan kumar
 
</script>

Output

7th Pentatope number :210
12th Pentatope number :1365

Time complexity: O(1)
Auxiliary space: O(1)

References: https://en.wikipedia.org/wiki/Pentatope_number/

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