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.
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 :
Below is the basic implementation of the above idea:
C++
#include <bits/stdc++.h>
using namespace std;
int center_nonadecagon_num( long int n )
{
return (19 * n * n - 19 * n + 2) / 2;
}
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
#include <stdio.h>
int center_nonadecagon_num( long int n )
{
return (19 * n * n - 19 * n + 2) / 2;
}
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;
}
|
Java
import java.io.*;
class GFG {
static int center_nonadecagon_num( int n)
{
return ( 19 * n * n - 19 * n + 2 ) / 2 ;
}
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));
}
}
|
Python3
def center_nonadecagon_num(n) :
return ( 19 * n * n -
19 * n + 2 ) / / 2
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))
|
C#
using System;
class GFG
{
static int center_nonadecagon_num( int n)
{
return (19 * n * n -
19 * n + 2) / 2;
}
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));
}
}
|
PHP
<?php
function center_nonadecagon_num( $n )
{
return (19 * $n * $n -
19 * $n + 2) / 2;
}
$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 );
?>
|
Javascript
<script>
function center_nonadecagon_num(n)
{
return (19 * n * n - 19 * n + 2) / 2;
}
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));
</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
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