Centered nonadecagonal number

Last Updated : 31 Mar, 2023

Given a number n, find the nth Centered Nonadecagonal number.
A Centered Nonadecagonal Number represents a dot in the center and other dots surrounding it in successive nonadecagon(19 sided polygon) layers.

center_nonadecagonalnum

The first few Centered Nonadecagonal numbers are:
1, 20, 58, 115, 191, 286, 400, 533, 685, 856, 1046, 1255.................................
Examples :

Input :  3
Output : 58 

Input : 13
Output :1483

In mathematics, Centered nonadecagonal number for n-th term is given by :

CN_{n}= (19n^2 - 19n +2)/2

Below is the basic implementation of the above idea:

C++

// C++ Program to find
// nth centered
// nonadecagonal number
#include <bits/stdc++.h>
using namespace std;

// centered nonadecagonal
//  function
int center_nonadecagon_num( long int n )
{
    // Formula to calculate nth
    // centered nonadecagonal number
    return (19 * n * n - 19 * n + 2) / 2;
}

// Driver Code
int main()
{
    long int n = 2;
    cout << n << "th centered nonadecagonal number : " 
                   << center_nonadecagon_num(n);
    cout << endl;
    n = 7;
    cout << n << "th centered nonadecagonal number : "
                  << center_nonadecagon_num(n);

    return 0;
}

// C Program to find
// nth centered
// nonadecagonal number
#include <stdio.h>

// centered nonadecagonal
//  function
int center_nonadecagon_num( long int n )
{
    // Formula to calculate nth
    // centered nonadecagonal number
    return (19 * n * n - 19 * n + 2) / 2;
}

// Driver Code
int main()
{
    long int n = 2;
    printf("%ldth centered nonadecagonal number : %d\n",n,center_nonadecagon_num(n));

    n = 7;
    printf("%ldth centered nonadecagonal number : %d\n",n,center_nonadecagon_num(n));

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

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

class GFG {
    
    // centered nonadecagonal
    // function
    static int center_nonadecagon_num(int n)
    {
        // Formula to calculate nth
        // centered nonadecagonal number
        return (19 * n * n - 19 * n + 2) / 2;
    }
    
    // Driver code
    public static void main (String[] args)
    {
        int n = 2;
        System.out.print ( n + "th centered "
                + "nonadecagonal number : ");
        System.out.println ( 
                   center_nonadecagon_num(n));
    
        n = 7;
        System.out.print ( n + "th centered "
                + "nonadecagonal number : ");
        System.out.println(
                  center_nonadecagon_num(n));
    }
}

// This code is contributed by m_kit

Python3

# Program to find nth
# centered nonadecagonal number
def center_nonadecagon_num(n) :
    
    # Formula to calculate 
    # nth centered nonadecagonal 
    # number & return it into 
    # main function.
    
    return (19 * n * n - 
            19 * n + 2) // 2

# Driver Code
if __name__ == '__main__' :
        
    n = 2
    print(n,"nd centered nonadecagonal " + 
                              "number : ", 
                center_nonadecagon_num(n))

    n = 7
    print(n,"nd centered nonadecagonal " + 
                              "number : ", 
                center_nonadecagon_num(n))

# This code is contributed by ajit

// C# Program to find 
// nth centered 
// nonadecagonal number
using System;

class GFG
{
    
    // centered nonadecagonal
    // function
    static int center_nonadecagon_num(int n)
    {
        // Formula to calculate nth
        // centered nonadecagonal number
        return (19 * n * n - 
                19 * n + 2) / 2;
    }
    
    // Driver code
    static public void Main ()
    {
        
        int n = 2;
        Console.Write ( n + "th centered " + 
                 "nonadecagonal number : ");
        Console.WriteLine(
                 center_nonadecagon_num(n));
    
        n = 7;
        Console.Write( n + "th centered " + 
                "nonadecagonal number : ");
        Console.WriteLine(
                center_nonadecagon_num(n));
    }
}

// This code is contributed by ajit

PHP

<?php
// PHP Program to find
// nth centered
// nonadecagonal number

// centered nonadecagonal
// function
function center_nonadecagon_num( $n )
{
    // Formula to calculate nth
    // centered nonadecagonal number
    return (19 * $n * $n - 
            19 * $n + 2) / 2;
}

// Driver Code
$n = 2;
echo $n ,"th centered " + 
         "nonadecagonal number : ",
        center_nonadecagon_num($n);
echo "\n";
$n = 7;
echo $n , "th centered " + 
          "nonadecagonal number : ",
         center_nonadecagon_num($n);
            
// This code is contributed by ajit
?>

JavaScript

<script>

// Javascript program to find nth centered
// nonadecagonal number

// centered nonadecagonal
// function
function center_nonadecagon_num(n)
{
    
    // Formula to calculate nth
    // centered nonadecagonal number
    return (19 * n * n - 19 * n + 2) / 2;
}

// Driver Code 
var n = 2;
document.write(n + "th centered " + 
               "nonadecagonal number : ");
document.write(center_nonadecagon_num(n) + "<br>");

n = 7;
document.write(n + "th centered " + 
               "nonadecagonal number : ");
document.write(center_nonadecagon_num(n));

// This code is contributed by Kirti
    
</script>

Output :

2nd centered nonadecagonal number : 20
7th centered nonadecagonal number : 400

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

References:
http://oeis.org/A069132

Centered Dodecagonal Number

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