Octagonal number

Last Updated : 20 Feb, 2023

You are given a number n, the task is to find n^th octagonal number. Also, find the Octagonal series till n.
An octagonal number is the figure number that represent octagonal. Octagonal numbers can be formed by placing triangular numbers on the four sides of a square. Octagonal number is calculated by using the formula (3n² – 2n).
Examples :

Input : 5  Output : 65    Input : 10  Output : 280    Input : 15  Output : 645

C++

   // C++ program to find 
// nth octagonal number 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to calculate 
//octagonal number 
int octagonal(int n) 
{ 
    // Formula for finding  
    // nth octagonal number 
    return 3 * n * n - 2 * n; 
} 
  
// Driver function 
int main() 
{ 
    int n = 10; 
    cout << n << "th octagonal number :" 
         << octagonal(n); 
    return 0; 
} 
 
  

Java

   // Java program to find 
// nth octagonal number 
import java.util.*; 
import java.lang.*; 
  
public class GfG { 
  
    // Function to calculate 
    //octagonal number 
    public static int octagonal(int n) 
    { 
        // Formula for finding  
        // nth octagonal number 
        return 3 * n * n - 2 * n; 
    } 
  
    // Driver function 
    public static void main(String argc[]) 
    { 
        int n = 10; 
        System.out.println(n + "th octagonal" + 
                     " number :" + octagonal(n)); 
    } 
} 
  
/* This code is contributed by Sagar Shukla */
 
  

Python

   # Python program to find  
# nth octagonal number 
def octagonal(n): 
    return 3 * n * n - 2 * n 
  
# Driver code 
n = 10
print(n, "th octagonal number :", 
       octagonal(n)) 
 
  

C#

   // C# program to find nth octagonal number 
using System; 
  
public class GfG { 
  
    // Function to calculate 
    //octagonal number 
    public static int octagonal(int n) 
    { 
          
        // Formula for finding  
        // nth octagonal number 
        return 3 * n * n - 2 * n; 
    } 
  
    // Driver function 
    public static void Main() 
    { 
        int n = 10; 
          
        Console.WriteLine(n + "th octagonal" 
              + " number :" + octagonal(n)); 
    } 
} 
  
/* This code is contributed by Vt_m */
 
  

PHP

   <?php 
// PHP program to find 
// nth octagonal number 
  
  
// Function to calculate 
//octagonal number 
function octagonal($n) 
{ 
      
    // Formula for finding  
    // nth octagonal number 
    return 3 * $n * $n - 2 * $n; 
} 
  
    // Driver Code 
    $n = 10; 
    echo $n , "th octagonal number :"
                     , octagonal($n); 
                       
// This code is contributed by Vt_m . 
?> 
 
  

Javascript

   <script> 
  
// JavaScript program to convert 
// Binary code to Gray code 
  
    // Function to calculate 
    //octagonal number 
    function octagonal(n) 
    { 
        // Formula for finding  
        // nth octagonal number 
        return 3 * n * n - 2 * n; 
    } 
   
// Driver code                    
        let n = 10; 
        document.write(n + "th octagonal" + 
                     " number :" + octagonal(n)); 
     
   // This code is contributed by code_hunt. 
</script> 
 
  

Output :

10th octagonal number : 280

Time Complexity: O(1)
Auxiliary Space: O(1)

Given number n, find the octagonal series till n.

We can also find the octagonal series. Octagonal series contains the points on octagonal.

Octagonal series 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, . . .

C++

   // C++ program to display the  
// octagonal series 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to display 
// octagonal series 
void octagonalSeries(int n) 
{ 
    // Formula for finding  
    //nth octagonal number 
    for (int i = 1; i <= n; i++)  
  
        // Formula for computing  
        // octagonal number 
        cout << (3 * i * i - 2 * i);     
} 
  
// Driver function 
int main() 
{ 
    int n = 10; 
    octagonalSeries(n); 
    return 0; 
} 
 
  

Java

   // Java program to find  
// nth octagonal number 
import java.util.*; 
import java.lang.*; 
   
public class GfG { 
   
    // Function to display octagonal series 
    public static void octagonalSeries(int n) 
    { 
        // Formula for finding  
        //nth octagonal number 
        for (int i = 1; i <= n; i++) 
   
            // Formula for computing 
            // octagonal number 
            System.out.print(3 * i * i - 2 * i); 
    } 
   
    // Driver function 
    public static void main(String argc[]) 
    { 
        int n = 10; 
        octagonalSeries(n); 
    } 
   
    /* This code is contributed by Sagar Shukla */
} 
 
  

Python

   # Python program to find  
# nth octagonal number 
def octagonalSeries(n): 
    for i in range(1, n + 1): 
        print(3 * i * i - 2 * i, 
                   end = ", ") 
  
# Driver code 
n = 10
octagonalSeries(n) 
 
  

C#

   // C# program to find  
// nth octagonal number 
using System; 
  
public class GfG { 
  
    // Function to display octagonal series 
    public static void octagonalSeries(int n) 
    { 
          
        // Formula for finding  
        //nth octagonal number 
        for (int i = 1; i <= n; i++) 
  
            // Formula for computing 
            // octagonal number 
            Console.Write(3 * i * i - 2 * i + ", "); 
    } 
  
    // Driver function 
    public static void Main() 
    { 
        int n = 10; 
          
        octagonalSeries(n); 
    } 
} 
  
/* This code is contributed by Vt_m */
 
  

PHP

   <?php 
// PHP program to display the  
// octagonal series 
  
  
// Function to display 
// octagonal series 
function octagonalSeries($n) 
{ 
      
    // Formula for finding  
    // nth octagonal number 
    for ($i = 1; $i <= $n; $i++)  
  
        // Formula for computing  
        // octagonal number 
        echo (3 * $i * $i - 2 * $i),",";  
} 
  
    // Driver Code 
    $n = 10; 
    octagonalSeries($n); 
  
// This code is contributed by Vt_m . 
?> 
 
  

Javascript

   <script> 
// Javascript program to display the 
// octagonal series 
  
  
// Function to display 
// octagonal series 
function octagonalSeries(n) 
{ 
      
    // Formula for finding 
    // nth octagonal number 
    for (let i = 1; i <= n; i++) 
  
        // Formula for computing 
        // octagonal number 
        document.write(3 * i * i - 2 * i + ", "); 
} 
  
    // Driver Code 
    let n = 10; 
    octagonalSeries(n); 
  
// This code is contributed by _saurabh_jaiswal 
  
</script>
 
  

Output :

1, 8, 21, 40, 65, 96, 133, 176, 225, 280

Time Complexity: O(n)
Auxiliary Space: O(1)

Centered Octagonal Number

dharmendra_kumar

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Octagonal number

C++

Java

Python

C#

PHP

Javascript

Given number n, find the octagonal series till n.

C++

Java

Python

C#

PHP

Javascript

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