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Program to print pentatope numbers upto Nth term
• Last Updated : 12 Apr, 2021

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 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

 

## Javascript

 
Output:
1 5 15 35 70 126 210 330 495 715

Time Complexity: O(n)
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 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

 

## Javascript

 
Output:
1 5 15 35 70 126 210 330 495 715

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