Nonagonal number

Last Updated : 07 Oct, 2021

A nonagonal number is a figurate number that extends the concept of triangular and square numbers to the nonagon. Specifically, the nth nonagonal numbers count the number of dots in a pattern of n nested nonagons (9 sided polygons), all sharing a common corner, where the ith nonagon in the pattern has sides made of i dots spaced one unit apart from each other.

Examples :

Input : n = 10
       n (7n - 5) / 2
       10 * (7 * 10 - 5) / 2
       10 * 65 / 2 = 325
Output :325

Input : 15
Output :750

The n^th nonagonal number is given by the formula: n (7n - 5) / 2.

C++

// CPP Program to find
// nth nonagonal number.
#include <bits/stdc++.h>
using namespace std;

// Function to find nth
// nonagonal number.
int Nonagonal(int n)
{
    // Formula to find nth 
    // nonagonal number.
    return n * (7 * n - 5) / 2;
}

// Driver function.
int main()
{
    int n = 10;    
    cout << Nonagonal(n);    
    return 0;
}

Java

// Java Program to find
// nth nonagonal number.
import java.io.*;

class GFG {
    
    // Function to find nth
    // nonagonal number.
    static int Nonagonal(int n)
    {
        // Formula to find nth 
        // nonagonal number.
        return n * (7 * n - 5) / 2;
    }
    
    // Driver function.
    public static void main(String args[])
    {
        int n = 10; 
        System.out.println(Nonagonal(n)); 
    }
}


// This code is contributed by Nikita Tiwari.

Python3

# Python 3 Program to find
# nth nonagonal number.

# Function to find nth
# nonagonal number.
def Nonagonal(n):
 
    # Formula to find nth 
    # nonagonal number.
    return int(n * (7 * n - 5) / 2) 
 
n = 10  
print(Nonagonal(n)) 

# This code is contributed by
# Smitha Dinesh Semwal

// C# Program to find
// nth nonagonal number.
using System;

class GFG {
    
    // Function to find nth
    // nonagonal number.
    static int Nonagonal(int n)
    {
        // Formula to find nth 
        // nonagonal number.
        return n * (7 * n - 5) / 2;
    }
    
    // Driver function.
    public static void Main()
    {
        int n = 10; 
        Console.Write(Nonagonal(n)); 
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP Program to find
// nth nonagonal number.

// Function to find nth
// nonagonal number.
function Nonagonal($n)
{
    // Formula to find nth 
    // nonagonal number.
    return $n * (7 * $n - 5) / 2;
}

// Driver Code
$n = 10; 
echo Nonagonal($n); 
    
// This code is contributed by vt_m.
?>

JavaScript

<script>
// Javascript Program to find
// nth nonagonal number.

// Function to find nth
// nonagonal number.
function Nonagonal(n)
{

    // Formula to find nth 
    // nonagonal number.
    return parseInt(n * (7 * n - 5) / 2);
}

// Driver function.
let n = 10;    
document.write(Nonagonal(n));

// This code is contributed by souravmahato348.
</script>

Output :

Time Complexity: O(1)

Auxiliary Space: O(1)

Given a number n, find nonagonal number series till n terms.

C++

// CPP Program find first
// n nonagonal number.
#include <bits/stdc++.h>
using namespace std;

// Function to find nonagonal
// number series.
int Nonagonal(int n)
{
    for (int i = 1; i <= n; i++) 
    {
        cout << i * (7 * i - 5) / 2;
        cout << " ";
    }
}

// Driver Code
int main()
{
    int n = 10;
    
    Nonagonal(n);
    
    return 0;
}

Java

// Java Program find first
// n nonagonal number.
import java.io.*;

class GFG 
{

    // Function to find nonagonal
    // number series.
    static void Nonagonal(int n)
    {
        for (int i = 1; i <= n; i++) 
        {
            System.out.print(i * (7 * 
                             i - 5) / 2);
            System.out.print(" ");
        }
    }

    // Driver Code
    public static void main(String args[])
    {
        int n = 10; 
        Nonagonal(n); 
    }
}

// This code is contributed
// by Nikita Tiwari.

Python3

# Python 3 Program find first
# n nonagonal number.

# Function to find nonagonal
# number series.
def Nonagonal(n):
 
    for i in range(1, n+1):  
        print(int(i * (7 * i - 5) / 2),end=" ") 
    
# driver Function     
n = 10 
Nonagonal(n) 
    
# This code is contributed by
# Smitha Dinesh Semwal

// C# Program find first
// n nonagonal number.
using System;

class GFG 
{

    // Function to find nonagonal
    // number series.
    static void Nonagonal(int n)
    {
        for (int i = 1; i <= n; i++) 
        {
            Console.Write(i * (7 * 
                          i - 5) / 2);
            Console.Write(" ");
        }
    }

    // Driver Code
    public static void Main()
    {
        int n = 10; 
        Nonagonal(n); 
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP Program find first
// n nonagonal number.

// Function to find nonagonal
// number series.
function Nonagonal($n)
{
    for ( $i = 1; $i <= $n; $i++) 
    {
        echo $i * (7 * $i - 5) / 2;
        echo " ";
    }
}

// Driver Code
$n = 10;

Nonagonal($n);

// This code is contributed by ajit
?>

JavaScript

<script>

// Javascript Program find first
// n nonagonal number.

// Function to find nonagonal
// number series.
function Nonagonal(n)
{
    for (let i = 1; i <= n; i++) 
    {
        document.write(parseInt(i * (7 * i - 5) / 2) + " ");
    }
}

// Driver Code
let n = 10;

Nonagonal(n);

</script>

Output :

1 9 24 46 75 111 154 204 261 325

Time Complexity: O(n)

Auxiliary Space: O(1)

Reference:https://en.wikipedia.org/wiki/Nonagonal_number

Analysis of Algorithms

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