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.
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