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++
#include <bits/stdc++.h>
using namespace std;
int Pentatope_number( int n)
{
return n * (n + 1) * (n + 2) * (n + 3) / 24;
}
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
import java.io.*;
class GFG {
static int Pentatope_number( int n)
{
return n * (n + 1 ) * (n + 2 ) *
(n + 3 ) / 24 ;
}
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));
}
}
|
Python3
def Pentatope_number(n):
return (n * (n + 1 ) * (n + 2 )
* (n + 3 ) / / 24 )
n = 7
print ( "%sth Pentatope number : " % n,
Pentatope_number(n))
n = 12
print ( "%sth Pentatope number : " % n,
Pentatope_number(n))
|
C#
using System;
class GFG {
static int Pentatope_number( int n)
{
return n * (n + 1) * (n + 2) *
(n + 3) / 24;
}
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));
}
}
|
PHP
<?php
function Pentatope_number( $n )
{
return $n * ( $n + 1) *
( $n + 2) * ( $n + 3)
/ 24;
}
$n = 7;
echo $n , "th Pentatope number :"
, Pentatope_number( $n ), "\n" ;
$n = 12;
echo $n , "th Pentatope number :"
, Pentatope_number( $n ) ;
?>
|
Javascript
<script>
function Pentatope_number(n)
{
return n * (n + 1) *(n + 2) * (n + 3)/ 24;
}
let n = 7;
document.write( n + "th "
+ "Pentatope number : "
+ Pentatope_number(n)+ "<br>" ) ;
n = 12;
document.write( n + "th "
+ "Pentatope number : "
+ Pentatope_number(n)) ;
</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/
Last Updated :
16 Oct, 2022
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