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: 35Input: 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// numberint Pentatope_number(int n){ // formula for find Pentatope // nth term return n * (n + 1) * (n + 2) * (n + 3) / 24;}// Driver Codeint 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// numberimport 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 numberdef Pentatope_number(n): # Formula to calculate nth # Pentatope number return (n * (n + 1) * (n + 2) * (n + 3) // 24)# Driver Coden = 7print("%sth Pentatope number : " %n, Pentatope_number(n))n = 12print("%sth Pentatope number : " %n, Pentatope_number(n))# This code is contributed by ajit. |
C#
// C# Program to find the nth Pentatope // numberusing 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// numberfunction 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// numberfunction 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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