Centered Square Number

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

Centered Square Number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. Nth Centered square number can be calculated by using formula n2 + (n-1)2.

Centered-Square-Number



Examples :

Input : n = 2
Output : 5

Input : n = 9
Output : 145

We can find n-th Centered Square Number using below formula.

n-th Centered Square Number = n2 + (n-1)2

How does this formula work?
If we take a closer look, we can notice that the n-th Centered Square Number can be seen as sum of two consecutive square numbers (1 dot, 4 dots, 9 dots, 16 dots, etc).

Below is the implementation :

C++

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// C++ program to find nth
// Centered square number.
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to calculate Centered
// square number function
int centered_square_num(int n)
{
    // Formula to calculate nth
    // Centered square number
    return n * n + ((n - 1) * (n - 1));
}
  
// Driver Code
int main()
{
    int n = 7;
    cout << n << "th Centered square number: ";
    cout << centered_square_num(n);
    return 0;
}

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Java

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// Java program to find nth Centered square
// number
import java.io.*;
  
class GFG {
  
    // Function to calculate Centered
    // square number function
    static int centered_square_num(int n)
    {
        // Formula to calculate nth
        // Centered square number
        return n * n + ((n - 1) * (n - 1));
    }
      
    // Driver Code
    public static void main (String[] args) 
    {
        int n = 7;
        System.out.print( n + "th Centered"
                       + " square number: "
                 + centered_square_num(n));
    }
}
  
// This code is contributed by anuj_67.

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Python3

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# Python program to find nth
# Centered square number.
  
  
# Function to calculate Centered
# square number function
def centered_square_num(n):
  
    # Formula to calculate nth
    # Centered square number
    return n * n + ((n - 1) * (n - 1))
  
  
# Driver Code
n = 7
print("%sth Centered square number: " %n,
                  centered_square_num(n))
     

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C#

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// C# program to find nth
// Centered square number.
using System;
  
public class GFG {
  
    // Function to calculate Centered
    // square number function
    static int centered_square_num(int n)
    {
        // Formula to calculate nth
        // Centered square number
        return n * n + ((n - 1) * (n - 1));
    }
      
    // Driver Code
  
    static public void Main (){
    int n = 7;
    Console.WriteLine( n + "th Centered"
                    + " square number: "
               + centered_square_num(n));
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// PHP program to find nth
// Centered square number
  
// Function to calculate Centered
// square number function
function centered_square_num( $n)
{
    // Formula to calculate nth
    // Centered square number
    return $n * $n + (($n - 1) * 
                      ($n - 1));
}
  
// Driver Code
$n = 7;
echo $n , "th Centered square number: ";
echo centered_square_num($n);
  
// This code is contributed by anuj_67.
?>

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Output :

7th Centered square number: 85

 
Reference : https://en.wikipedia.org/wiki/Centered_square_number



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