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Centered triangular number
  • Difficulty Level : Basic
  • Last Updated : 31 Oct, 2018

Given an integer n, find the nth Centered triangular number.

Centered Triangular Number is a centered polygonal number that represents a triangle with a dot in the centre and all other dots surrounding the centre in successive triangular layers [Source : Wiki ]

Pictorial Representation :
centered Trigunal number pic

The first few centered triangular number series are :
1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460………………………..

Examples:



Input : n = 1
Output : 4
Explanation :
A dot in the centre and 3 dots forming the
triangle outside it, thus 4.

Input : n = 6 
Output : 64

Input : n = 10
Output : 166

Approach
nth Term of centered triangular number is given by:

 CT_{n}=(3n^2+3n+2)/2 

Basic Implementation of the above approach:

C++

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// CPP Program to find the
// nth Centered Trigunal number
#include 
using namespace std;
  
// function for Centered
// Trigunal number
int Centered_Trigunal_num(int n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * n * n + 3 * n + 2) / 2;
}
  
// Driver Code
int main()
{
    // For 3rd Centered Trigunal number
    int n = 3;
    cout << Centered_Trigunal_num(n) << endl;
  
    // For 12th Centered Trigunal number
    n = 12;
    cout << Centered_Trigunal_num(n) << endl;
  
    return 0;
}

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Java

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// Java Program to find 
// the nth Centered 
// Triangular number
import java.io.*;
  
class GFG 
{
      
// function for Centered
// Trigunal number
static int Centered_Trigunal_num(int n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * n * n + 
            3 * n + 2) / 2;
}
  
// Driver Code
public static void main (String[] args) 
{
  
// For 3rd Centered 
// Trigunal number
int n = 3;
System.out.println(Centered_Trigunal_num(n));
  
// For 12th Centered 
// Trigunal number
n = 12;
System.out.println(Centered_Trigunal_num(n));
}
}
  
// This code is contributed by ajit

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Python3

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# Program to find nth 
# Centered Trigunal number
  
def Centered_Trigunal_num(n) :
      
    # Formula to calculate nth
    # Centered Trigunal number
    return (3 * n * n + 
            3 * n + 2) // 2
  
# Driver Code
if __name__ == '__main__' :
  
    # For 3rd Centered 
    # Trigunal number     
    n = 3
    print(Centered_Trigunal_num(n))
      
    # For 12th Centered
    # Trigunal number
    n = 12
    print(Centered_Trigunal_num(n))
                  
                  
# This code is contributed 
# by akt_mit

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C#

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// C# Program to find 
// the nth Centered 
// Triangular number
using System;
  
class GFG
{
  
// function for Centered
// Trigunal number
static int Centered_Trigunal_num(int n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * n * n + 
            3 * n + 2) / 2;
}
  
// Driver Code
static public void Main ()
{
  
// For 3rd Centered 
// Trigunal number
int n = 3;
Console.WriteLine(Centered_Trigunal_num(n));
  
// For 12th Centered 
// Trigunal number
n = 12;
Console.WriteLine(Centered_Trigunal_num(n));
}
}
  
// This code is contributed by akt_mit

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PHP

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<?php
// PHP Program to find the
//nth Centered Trigunal number
  
// function for Centered
// Trigunal number
function Centered_Trigunal_num($n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * $n * $n + 3 * $n + 2) / 2;
}
  
// Driver Code
    // For 3rd Centered Trigunal number
    $n = 3;
    echo Centered_Trigunal_num($n), "\n" ;
  
    // For 12th Centered Trigunal number
    $n = 12;
    echo Centered_Trigunal_num($n), "\n";
  
// This code is contributed by aj_36
?>

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Output :

19
235

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