# Program to print tetrahedral numbers upto Nth term

• Last Updated : 25 May, 2022

Prerequisites:

Given a value n, and the task is to print tetrahedral number series up to nth term.
Examples:

Input: 5
Output: 1  4  10  20  35

Input: 10
Output: 1  4  10  20  35  56  84  120  165  220 

Method 1: Using Triangular Number series:
This problem can be easily solved with the fact that Nth Tetrahedral Number is equal to the sum of first N Triangular Numbers.
Let’s have a look on Series of triangular and tetrahedral Numbers.

To print series upto 5th term:
Triangular Numbers  =  1        3          6             10                  15
Tetrahedral numbers =  1        4          10            20                  35
i.e  (1)    (1 + 3)  (1 + 3 + 6)  (1 + 3 + 6 + 10)  (1 + 3 + 6 + 10 + 35)   

Calculate Nth Triangular number using formula So, print the tetrahedral numbers series by generating triangular numbers and adding it with the sum of all previously generated triangular numbers.
Below is the implementation of the above approach:

## C++

 // C++ program to generate tetrahedral // number series #include  using namespace std;   // function to generate nth triangular // number long findTriangularNumber(int n) {     return (n * (n + 1)) / 2; }   // function to print tetrahedral number  // series up to n void printSeries(int n) {     // Initialize prev as 0. It stores      // the sum of all previously generated     // triangular number     int prev = 0;     int curr;       // Loop to print series     for (int i = 1; i <= n; i++)      {         // Find ith triangular number         curr = findTriangularNumber(i);           // Add ith triangular number to         // sum of all previously generated         // triangular number to get ith          // tetrahedral number         curr = curr + prev;         cout << curr << " ";           // Update sum of all previously          // generated triangular number         prev = curr;     } }   // Driver code int main() {     int n = 10;           // function call to print series     printSeries(n);           return 0; }

## Java

 // Java program to generate tetrahedral // number series import java.io.*;   class GFG {           // function to generate nth triangular     // number     static long findTriangularNumber(int n)     {         return (n * (n + 1)) / 2;     }           // function to print tetrahedral number      // series up to n     static void printSeries(int n)     {         // Initialize prev as 0. It store          // the sum of all previously generated         // triangular number         long prev = 0;         long curr;               // Loop to print series         for (int i = 1; i <= n; i++)          {             // Find ithh triangular number             curr = findTriangularNumber(i);                   // Add ith triangular number to             // sum of all previously generated             // triangular number to get ith              // tetrahedral number             curr = curr + prev;             System.out.print(curr + " ");                   // Update sum of all previously              // generated triangular number             prev = curr;         }     }       // Driver code     public static void main (String[] args)      {         int n = 10;               // function call to print series         printSeries(n);     } }

## Python3

 # Python3 program to generate  # tetrahedral number series   # function to generate nth  # triangular number def findTriangularNumber(n):     return (n * (n + 1)) / 2   # function to print tetrahedral  # number series up to n def printSeries(n):       # Initialize prev as 0.      # It stores the sum of all      # previously generated      # triangular number     prev = 0       # Loop to print series     for i in range(1, n+1):                # Find ith triangular number         curr = findTriangularNumber(i)           # Add ith triangular number          # to sum of all previously          # generated triangular number          # to get ith tetrahedral number         curr = int(curr + prev)         print(curr, end = ' ')           # Update sum of all previously          # generated triangular number         prev = curr   # Driver code n = 10       # function call to # print series printSeries(n)   # This code is contributed by Mahadev.

## C#

 // C# program to generate tetrahedral // number series using System;   public class GFG{           // function to generate nth triangular     // number     static long findTriangularNumber(int n)     {         return (n * (n + 1)) / 2;     }           // function to print tetrahedral number      // series up to n     static void printSeries(int n)     {         // Initialize prev as 0. It store          // the sum of all previously generated         // triangular number         long prev = 0;         long curr;               // Loop to print series         for (int i = 1; i <= n; i++)          {             // Find ithh triangular number             curr = findTriangularNumber(i);                   // Add ith triangular number to             // sum of all previously generated             // triangular number to get ith              // tetrahedral number             curr = curr + prev;             Console.Write(curr + " ");                   // Update sum of all previously              // generated triangular number             prev = curr;         }     }       // Driver code     static public void Main ()     {         int n = 10;               // function call to print series         printSeries(n);     } }

## PHP

 

## Javascript

 

Output:

1 4 10 20 35 56 84 120 165 220

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 Tetrahedral Number Formula:
Formula to find nth tetrahedral number: Below is the required implementation:

## C++

 // C++ program to generate series of  // tetrahedral numbers #include  using namespace std;   // function to print tetrahedral  // number series up to n void printSeries(int n) {       // loop to print series     for (int i = 1; i <= n; i++)     {         // Calculate and print ith          // tetrahedral number                 int num = i * (i + 1) * (i + 2) / 6;         cout << num << " ";     } }   // Driver code int main() {     int n = 10;           // function call to print series     printSeries(n);           return 0; }

## Java

 // Java program to generate series of  // tetrahedral numbers import java.io.*;   class GFG {           // function to print tetrahedral      // number series up to n     static void printSeries(int n)     {               // loop to print series         for (int i = 1; i <= n; i++)         {             // Calculate and print ith              // tetrahedral number             int num = i * (i + 1) * (i + 2) / 6;                           System.out.print(num + " ");         }     }           // Driver code     public static void main (String[] args)      {         int n = 10;               // function call to print series         printSeries(n);     } }

## Python3

 # Python3 code to print tetrahedral # numbers series up to n    # function to print tetrahedral series up to n def printSeries(n):        # loop to print series      for i in range(1, n + 1):                   # Calculate and print ith          # Tetrahedral number         num = i * (i + 1) * (i + 2) // 6                   print(num, end =' ')                     # Driver code n = 10   # function call to print series printSeries(n)

## C#

 // C# program to generate series of  // tetrahedral numbers using System;   public class GFG{           // function to print tetrahedral      // number series up to n     static void printSeries(int n)     {               // loop to print series         for (int i = 1; i <= n; i++)         {             // Calculate and print ith              // tetrahedral number             int num = i * (i + 1) * (i + 2) / 6;                           Console.Write(num + " ");         }     }           // Driver code     static public void Main ()     {         int n = 10;               // function call to print series         printSeries(n);     } }

## PHP

 

## Javascript

 

Output:

1 4 10 20 35 56 84 120 165 220

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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