Centered tridecagonal number

Given a number n, the task is to find the nth Centered Tridecagonal Number.

A Centered tridecagonal number represents a dot at the center and other dots surrounding the center dot
in the successive tridecagonal(13 sided polygon) layer.

Examples :

Input : 2
Output : 14

Input : 9
Output : 469

centered tridecagonal number



Formula for nth Centered tridecagonal number:

 CT_{n}= (13n(n-1)+2)/2 

C++

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// C++ Program to find nth
// centered tridecagonal number
#include <bits/stdc++.h>
using namespace std;
  
// Function to find nth centered
// tridecagonal number
int centeredTridecagonalNum(long int n)
{
    // Formula to calculate nth
    // centered tridecagonal number
    return (13 * n * (n - 1) + 2) / 2;
}
  
// Drivers code
int main()
{
    long int n = 3;
    cout << centeredTridecagonalNum(n);
    cout << endl;
    n = 10;
    cout << centeredTridecagonalNum(n);
  
    return 0;
}

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Java

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// Java Program to find nth
// centered tridecagonal number
import java.io.*;
  
class GFG 
{
  
// Function to find nth centered
// tridecagonal number
static long centeredTridecagonalNum(long n)
{
    // Formula to calculate nth
    // centered tridecagonal number
    return (13 * n * (n - 1) + 2) / 2;
}
  
// Driver Code
public static void main (String[] args) 
{
    long n = 3;
    System.out.println(centeredTridecagonalNum(n));
    n = 10;
    System.out.println(centeredTridecagonalNum(n));
}
}
  
// This code is contributed by anuj_67.

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Python3

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# Program to find nth centered 
# tridecagonal number
  
# Function to find centered
# tridecagonal number
def centeredTridecagonalNum(n) :
      
    # Formula to calculate nth
    # centered tridecagonal number
    return (13 * n * 
           (n - 1) + 2) // 2
  
# Driver Code
if __name__ == '__main__' :
          
    n = 3
    print(centeredTridecagonalNum(n))
    n = 10
    print(centeredTridecagonalNum(n))
                  
# This code is contributed
# by akt_mit

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C#

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// C# Program to find nth
// centered tridecagonal number
using System;
  
class GFG 
{
  
// Function to find nth centered
// tridecagonal number
static long centeredTridecagonalNum(long n)
{
    // Formula to calculate nth
    // centered tridecagonal number
    return (13 * n * (n - 1) + 2) / 2;
}
  
// Driver Code
public static void Main () 
{
    long n = 3;
    Console.WriteLine(centeredTridecagonalNum(n));
    n = 10;
    Console.WriteLine(centeredTridecagonalNum(n));
}
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// PHP Program to find nth
// centered tridecagonal number
  
// Function to find nth centered
// tridecagonal number
function centeredTridecagonalNum( $n)
{
    // Formula to calculate nth
    // centered tridecagonal number
    return (13 * $n
           ($n - 1) + 2) / 2;
}
  
// Driver Code
$n = 3;
echo centeredTridecagonalNum($n);
echo"\n";
  
$n = 10;
echo centeredTridecagonalNum($n);
  
// This code is contributed by anuj_67.
?>

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Output :

40
586

Reference: http://oeis.org/wiki/Figurate_numbers



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