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Program to print tetrahedral numbers upto Nth term

  • Last Updated : 07 May, 2021

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 \frac{N \times (N + 1)}{2}
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 <bits/stdc++.h>
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




<?php
// PHP program to generate tetrahedral
// number series
 
// function to generate nth triangular
// number
function findTriangularNumber($n)
{
    return ($n * ($n + 1)) / 2;
}
 
// function to print tetrahedral number
// series up to n
function printSeries($n)
{
    // Initialize prev as 0. It store
    // the sum of all previously generated
    // triangular number
    $prev = 0;
    $curr;
 
    // Loop to print series
    for ($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 + $prev;
        echo($curr . " ");
 
        // Update sum of all previously
        // generated triangular number
        $prev = $curr;
    }
}
 
// Driver code
$n = 10;
     
// function call to print series
printSeries($n);
?>

Javascript




<script>
// Javascript program to generate tetrahedral
// number series
 
// function to generate nth triangular
// number
function findTriangularNumber(n)
{
    return (n * (n + 1)) / 2;
}
 
// function to print tetrahedral number
// series up to n
function printSeries(n)
{
 
    // Initialize prev as 0. It stores
    // the sum of all previously generated
    // triangular number
    var prev = 0;
    var curr;
 
    // Loop to print series
    for (var 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;
        document.write( curr + " ");
 
        // Update sum of all previously
        // generated triangular number
        prev = curr;
    }
}
 
// Driver code
var n = 10;
 
// function call to print series
printSeries(n);
 
// This code is contributed by itsok.
</script>
Output: 
1 4 10 20 35 56 84 120 165 220

 

Time Complexity: O(n)
Method 2: Using Tetrahedral Number Formula: 
Formula to find nth tetrahedral number:\frac{N\times (N+1)\times (N+2)}{6}
Below is the required implementation:
 

C++




// C++ program to generate series of
// tetrahedral numbers
#include <bits/stdc++.h>
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




<?php
// PHP program to generate series of
// tetrahedral numbers
 
// function to print tetrahedral
// number series up to n
function printSeries($n)
{
 
    // loop to print series
    for ($i = 1; $i <= $n; $i++)
    {
        // Calculate and print ith
        // tetrahedral number
        $num = $i * ($i + 1) * ($i + 2) / 6;
        echo ($num . " ");
    }
}
 
// Driver code
$n = 10;
     
// function call to print series
printSeries($n);
 
?>

Javascript




<script>
 
// Javascript program to generate series of
// tetrahedral numbers
 
    // function to print tetrahedral
    // number series up to n
    function printSeries(n)
    {
      let i;
       
        // loop to print series
        for (i = 1; i <= n; i++)
        {
            // Calculate and print ith
            // tetrahedral number
            let num = i * (i + 1) * ((i + 2) / 6);
               
            document.write(num + " ");
        }
    }
 
// driver program
     
        let n = 10;
       
        // function call to print series
        printSeries(n);
  
 // This code is contributed by susmitakundugoaldanga.
</script>
Output: 
1 4 10 20 35 56 84 120 165 220

 


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