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Centered Pentadecagonal Number

  • Last Updated : 20 Jul, 2021

Given a number n, find the nth Centered Pentadecagonal Number . 
A Centered Pentadecagonal Number represents a dot in the centre and other dots surrounding it in successive pentadecagonal(15-sided polygon) layers.
 

centered pentadecagonal number

Examples :
 

Input :  2
Output : 16

Input : 8
Output : 421

 

n-th term of Centered pentadecagonal number:-
 



PD_{n}= (15n^2 -15n+2)/2

Below is the basic implementation of the above idea.
 

C++




// C++ Program to find
// nth centered
// pentadecagonal  number
#include <bits/stdc++.h>
using namespace std;
 
// centered pentadecagonal function
int center_pentadecagonal_num(long int n)
{
    // Formula to calculate nth
    // centered pentadecagonal number
    return (15 * n * n - 15 * n + 2) / 2;
}
 
// Driver Code
int main()
{
    long int n = 3;
    cout << n << "th number : "
             << center_pentadecagonal_num(n);
    cout << endl;
    n = 10;
    cout << n << "th number : "
             << center_pentadecagonal_num(n);
 
    return 0;
}

Java




// Java Program to find nth centered
// pentadecagonal number
 
import java.io.*;
 
class GFG {
     
    // centered pentadecagonal function
    static long center_pentadecagonal_num(long n)
    {
     
        // Formula to calculate nth
        // centered pentadecagonal number
        return (15 * n * n - 15 * n + 2) / 2;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
     
        long n = 3;
        System.out.print(n + "th number : ");
        System.out.println(
                  center_pentadecagonal_num(n));
         
        n = 10;
        System.out.print( n + "th number : ");
        System.out.println(
                 center_pentadecagonal_num(n));
    }
}
 
// This code is contributed by ajit.

Python3




# Program to find nth
#centered pentadecagonal number
 
def center_pentadecagonal_num(n) :
     
    # Formula to calculate nth
    # centered pentadecagonal number
    return (15 * n * n - 15 * n + 2) // 2
 
# Driver Code
if __name__ == '__main__' :
         
    n = 3
    print(n,"rd number : ",
                center_pentadecagonal_num(n))
    n = 10
    print(n,"th number : ",
                 center_pentadecagonal_num(n))
                  
 
# This code is contributed  by m_kit

C#




// C# Program to find
// nth centered
// pentadecagonal number
using System;
 
class GFG
{
     
    // centered
    // pentadecagonal function
    static long center_pentadecagonal_num(long n)
    {
     
        // Formula to calculate
        // nth centered
        // pentadecagonal number
        return (15 * n * n -
                15 * n + 2) / 2;
    }
     
    // Driver Code
    static public void Main ()
    {
        long n = 3;
        Console.Write(n + "th number : ");
        Console.WriteLine(
                center_pentadecagonal_num(n));
         
        n = 10;
        Console.Write( n + "th number : ");
        Console.WriteLine(
                center_pentadecagonal_num(n));
    }
}
 
// This code is contributed by ajit.

PHP




<?php
// PHP Program to find
// nth centered
// pentadecagonal number
 
// centered pentadecagonal function
function center_pentadecagonal_num($n)
{
    // Formula to calculate nth
    // centered pentadecagonal number
    return (15 * $n * $n -
            15 * $n + 2) / 2;
}
 
// Driver Code
$n = 3;
echo $n , "th number : ",
        center_pentadecagonal_num($n);
echo "\n";
$n = 10;
echo $n , "th number : ",
        center_pentadecagonal_num($n);
 
// This code is contributed by m_kit
?>

Javascript




<script>
 
// Javascript program to find nth centered
// pentadecagonal number
 
// centered pentadecagonal function
function center_pentadecagonal_num(n)
{
     
    // Formula to calculate nth
    // centered pentadecagonal number
    return (15 * n * n - 15 * n + 2) / 2;
}
 
// Driver Code
var n = 3;
document.write(n + "th number : ");
document.write(center_pentadecagonal_num(n) + "<br>");
 
n = 10;
document.write( n + "th number : ");
document.write(center_pentadecagonal_num(n));
                  
// This code is contributed by Kirti
     
</script>

Output : 

3th number : 46
10th number : 676

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

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