Pentatope number

Given a number n, the task is to write a program to find Nth pentatope number. A pentatope number is class of figurative number and can be represented as regular and discrete geometric patterns. In pascal triangle’s the number in the fifth cell of any row starting with 5-th term row 1 4 6 4 1 from right to left or left to right is Pentatope number.

Examples :

Input : 5
Output :70

Input :8
Output :1001

First few Pentatope numbers are:
1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001………

Formula for Nth Pentatope number:

      \begin{math}  Ptop_{n}=(n(n+1)(n+2)(n+3))/24 \end{math} 

C++

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// C++ Program to find the
// nth Pentatope Number
#include <bits/stdc++.h>
using namespace std;
  
// Function that returns nth
// pentatope number
int pentatopeNum(int n)
{
    return (n * (n + 1) * (n + 2) * (n + 3)) / 24;
}
  
// Drivers Code
int main()
{
    // For 5th PentaTope Number
    int n = 5;
    cout << pentatopeNum(n) << endl;
  
    // For 11th PentaTope Number
    n = 11;
    cout << pentatopeNum(n) << endl;
  
    return 0;
}

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Java

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// Java Program to find the
// nth Pentatope Number
import java.io.*;
  
class GFG 
{
      
// Function that returns nth
// pentatope number
static int pentatopeNum(int n)
{
    return (n * (n + 1) * 
           (n + 2) * (n + 3)) / 24;
}
// Driver Code
public static void main (String[] args) 
{
// For 5th PentaTope Number
int n = 5;
System.out.println(pentatopeNum(n));
  
// For 11th PentaTope Number
n = 11;
System.out.println(pentatopeNum(n));
  
}
}
  
// This code is contributed by m_kit

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Python3

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# Python3 program to find
# nth Pentatope number
  
# Function to calculate
# Pentatope number
def pentatopeNum(n):
  
    # Formula to calculate nth
    # Pentatope number
    return (n * (n + 1) * 
                (n + 2) * 
                (n + 3) // 24)
  
# Driver Code
n = 5
print(pentatopeNum(n))
n = 11
print(pentatopeNum(n))
  
# This code is contributed
# by ajit. 

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C#

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// C# Program to find the
// nth Pentatope Number
using System;
  
class GFG 
{
      
// Function that returns
// nth pentatope number
static int pentatopeNum(int n)
{
    return (n * (n + 1) * 
           (n + 2) * (n + 3)) / 24;
}
  
// Driver Code
static public void Main(String []args) 
{
      
// For 5th PentaTope Number
int n = 5;
  
Console.WriteLine(pentatopeNum(n));
  
// For 11th PentaTope Number
n = 11;
  
Console.WriteLine(pentatopeNum(n));
}
}
// This code is contributed by Arnab Kundu

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PHP

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<?php
// PHP Program to find the
// nth Pentatope Number
  
// Function that returns 
// nth pentatope number
function pentatopeNum($n)
{
    return ($n * ($n + 1) * 
                 ($n + 2) * 
                 ($n + 3)) / 24;
}
  
// Driver Code
  
// For 5th PentaTope Number
$n = 5;
echo pentatopeNum($n), "\n";
  
// For 11th PentaTope Number
$n = 11;
echo pentatopeNum($n), "\n" ;
  
// This code is contributed
// by aj_36
?>

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Output :

70
1001

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



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