Prerequisites:
Given a value n, and the task is to print pentatope numbers series up to nth term.
Examples:
Input: 5 Output: 1 5 15 35 70 Input: 10 Output: 1 5 15 35 70 126 210 330 495 715
Method 1: Using Tetrahedral Number Series:
This problem can be easily solved with the fact that Nth Pentatope Number is equal to the sum of first N Tetrahedral numbers.
Let’s have a look on Series of Pentatope and Tetrahedral Numbers.
For n = 5
Tetrahedral Numbers = 1, 4, 10, 20, 35
Prefix Sum of Tetrahedral numbers for each term: (1), (1 + 4), (1 + 4 + 10), (1 + 4 + 10 + 20), (1 + 4 + 10 + 20 + 35)
So, Pentatope numbers are 1, 5, 15, 35, 70
Calculate Nth Tetrahedral number using formula: 
So, print the Pentatope Numbers series by generating tetrahedral numbers and adding it with the sum of all previously generated Tetrahedral Numbers.
Below is the implementation of above approach:
CPP
// C++ program to generate Pentatope// Number series#include <bits/stdc++.h>using namespace std;// Function to generate nth tetrahedral numberint findTetrahedralNumber(int n){ return ((n * (n + 1) * (n + 2)) / 6);}// Function to print pentatope number // series upto nth term.void printSeries(int n){ // Initialize prev as 0. It store the // sum of all previously generated // pentatope numbers int prev = 0; int curr; // Loop to print pentatope series for (int i = 1; i <= n; i++) { // Find ith tetrahedral number curr = findTetrahedralNumber(i); // Add ith tetrahedral number to // sum of all previously generated // tetrahedral number to get ith // pentatope number curr = curr + prev; cout << curr << " "; // Update sum of all previously // generated tetrahedral number prev = curr; }}// Driver codeint main(){ int n = 10; // Function call to print pentatope // number series printSeries(n); return 0;} |
Java
// Java program to generate Pentatope// Number seriesimport java.io.*;class GFG { // Function to generate nth tetrahedral number static int findTetrahedralNumber(int n) { return ((n * (n + 1) * (n + 2)) / 6); } // Function to print pentatope number // series upto nth term. static void printSeries(int n) { // Initialize prev as 0. It store the // sum of all previously generated // pentatope numbers int prev = 0; int curr; // Loop to print pentatope series for (int i = 1; i <= n; i++) { // Find ith tetrahedral number curr = findTetrahedralNumber(i); // Add ith tetrahedral number to // sum of all previously generated // tetrahedral number to get ith // pentatope number curr = curr + prev; System.out.print(curr + " "); // Update sum of all previously // generated tetrahedral number prev = curr; } } // Driver code public static void main (String[] args) { int n = 10; // Function call to print pentatope // number series printSeries(n); }} |
python3
# Python program to generate Pentatope# Number series# Function to generate nth tetrahedral numberdef findTetrahedralNumber(n) : return (int((n * (n + 1) * (n + 2)) / 6))# Function to print pentatope number # series upto nth term.def printSeries(n) : # Initialize prev as 0. It store the # sum of all previously generated # pentatope numbers prev = 0 # Loop to print pentatope series for i in range(1, n + 1) : # Find ith tetrahedral number curr = findTetrahedralNumber(i) # Add ith tetrahedral number to # sum of all previously generated # tetrahedral number to get ith # pentatope number curr = curr + prev; print(curr, end=' ') # Update sum of all previously # generated tetrahedral number prev = curr# Driver coden = 10 # Function call to print pentatope# number seriesprintSeries(n) |
C#
// C# program to generate Pentatope// Number seriesusing System;public class GFG { // Function to generate nth tetrahedral number static int findTetrahedralNumber(int n) { return ((n * (n + 1) * (n + 2)) / 6); } // Function to print pentatope number // series upto nth term. static void printSeries(int n) { // Initialize prev as 0. It store the // sum of all previously generated // pentatope numbers int prev = 0; int curr; // Loop to print pentatope series for (int i = 1; i <= n; i++) { // Find ith tetrahedral number curr = findTetrahedralNumber(i); // Add ith tetrahedral number to // sum of all previously generated // tetrahedral number to get ith // pentatope number curr = curr + prev; Console.Write(curr + " "); // Update sum of all previously // generated tetrahedral number prev = curr; } } // Driver code static public void Main () { int n = 10; // Function call to print pentatope // number series printSeries(n); }} |
PHP
<?php// PHP program to generate Pentatope// Number series// Function to generate nth tetrahedral numberfunction findTetrahedralNumber($n){ return (($n * ($n + 1) * ($n + 2)) / 6);}// Function to print pentatope number // series upto nth term.function printSeries($n){ // Initialize prev as 0. It store the // sum of all previously generated // pentatope numbers $prev = 0; $curr; // Loop to print pentatope series for ($i = 1; $i <= $n; $i++) { // Find ith tetrahedral number $curr = findTetrahedralNumber($i); // Add ith tetrahedral number to // sum of all previously generated // tetrahedral number to get ith // pentatope number $curr = $curr + $prev; echo($curr . " "); // Update sum of all previously // generated tetrahedral number $prev = $curr; }}// Driver code$n = 10; // Function call to print pentatope// number seriesprintSeries($n);?> |
Javascript
<script>// JavaScript program to generate Pentatope// Number series// Function to generate nth tetrahedral numberfunction findTetrahedralNumber(n){ return ((n * (n + 1) * (n + 2)) / 6);}// Function to print pentatope number// series upto nth term.function printSeries(n){ // Initialize prev as 0. It store the // sum of all previously generated // pentatope numbers let prev = 0; let curr; // Loop to print pentatope series for (let i = 1; i <= n; i++) { // Find ith tetrahedral number curr = findTetrahedralNumber(i); // Add ith tetrahedral number to // sum of all previously generated // tetrahedral number to get ith // pentatope number curr = curr + prev; document.write(curr+" "); // Update sum of all previously // generated tetrahedral number prev = curr; }}// Driver codelet n = 10; // Function call to print pentatope// number seriesprintSeries(n);// This code is contributed by sravan kumar</script> |
Output:
1 5 15 35 70 126 210 330 495 715
Time Complexity: O(n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
Method 2: Using Pentatope Number Formula:
The formula to find Nth Pentatope number 
Below is the required implementation:
CPP
// C++ program to print Pentatope number series.#include <bits/stdc++.h>using namespace std;// Function to print pentatope series up to nth termvoid printSeries(int n){ // Loop to print pentatope number series for (int i = 1; i <= n; i++) { // calculate and print ith pentatope number int num = (i * (i + 1) * (i + 2) * (i + 3) / 24); cout << num << " "; }}// Driver codeint main(){ int n = 10; // Function call to print pentatope number series printSeries(n); return 0;} |
Java
// Java program to print Pentatope number series.import java.io.*;class GFG { // Function to print pentatope series up to nth term static void printSeries(int n) { // Loop to print pentatope number series for (int i = 1; i <= n; i++) { // calculate and print ith pentatope number int num = (i * (i + 1) * (i + 2) * (i + 3) / 24); System.out.print(num + " "); } } // Driver code public static void main (String[] args) { int n = 10; // Function call to print pentatope number series printSeries(n); }} |
python3
# Python program to print Pentatope number series.# Function to print pentatope series up to nth termdef printSeries(n) : # Loop to print pentatope number series for i in range(1, n + 1) : # calculate and print ith pentatope number num = int(i * (i + 1) * (i + 2) * (i + 3) // 24) print(num, end=' ');# Driver coden = 10 # Function call to print pentatope number seriesprintSeries(n) |
C#
// C# program to print Pentatope number series.using System;public class GFG { // Function to print pentatope series up to nth term static void printSeries(int n) { // Loop to print pentatope number series for (int i = 1; i <= n; i++) { // calculate and print ith pentatope number int num = (i * (i + 1) * (i + 2) * (i + 3) / 24); Console.Write(num + " "); } } // Driver code static public void Main () { int n = 10; // Function call to print pentatope number series printSeries(n); }} |
PHP
<?php// PHP program to print Pentatope number series.// Function to print pentatope series up to nth termfunction printSeries($n){ // Loop to print pentatope number series for ($i = 1; $i <= $n; $i++) { // calculate and print ith pentatope number $num = ($i * ($i + 1) * ($i + 2) * ($i + 3) / 24); echo($num . " "); }}// Driver code$n = 10; // Function call to print pentatope number seriesprintSeries($n);?> |
Javascript
<script>// Javascript program to print Pentatope number series.// Function to print pentatope series up to nth termfunction printSeries(n){ // Loop to print pentatope number series for (let i = 1; i <= n; i++) { // calculate and print ith pentatope number num = (i * (i + 1) * (i + 2) * (i + 3) / 24); document.write(num+" "); }}// Driver codelet n = 10; // Function call to print pentatope number seriesprintSeries(n);// This code is contributed by sravan kumar</script> |
Output:
1 5 15 35 70 126 210 330 495 715
Time Complexity: O(n), where n represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!