Decagonal Numbers

You are given a number n, the task is to find the nth Decagonal number. A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). The nth decagonal numbers counts the number of dots in a pattern of n nested decagons, all sharing a common corner, where the ith decagon in the pattern has sides made of i dots spaced one unit apart from each other.

Examples: 

Input : n = 3
Output : 27

Input : n = 7
Output : 175
 

The n-th decagonal number is given by the formula 
(4n ² – 3n). 

C++

// C++ program to find nth decagonal number
#include <bits/stdc++.h>
using namespace std;

// Function to calculate decagonal number
int decagonal(int n)
{
    // Formula for finding nth decagonal number
    return 4 * n * n - 3 * n;
}

// Driver function
int main()
{
    int n = 10;
    cout << n << "th decagonal number :" << decagonal(n);
    return 0;
}

Java

// JAVA Code for Decagonal Numbers
import java.util.*;

class GFG {

    // Function to calculate
    // decagonal number
    static int decagonal(int n)
    {
        // Formula for finding nth
        // decagonal number
        return 4 * n * n - 3 * n;
    }

    /* Driver function */
    public static void main(String[] args)
    {
        int n = 10;
        System.out.println(n + "th decagonal number :"
                            + decagonal(n));
    }
}

// This code is contributed by Arnav Kr. Mandal.

Python

# Python program to find nth decagonal number
def decagonal(n):
    return 4 * n * n - 3 * n

# Driver code
n = 10
print(n, "th decagonal number :", decagonal(n))

C#

// C# Code for Decagonal Numbers
using System;

class GFG {

    // Function to calculate
    // decagonal number
    static int decagonal(int n)
    {
        // Formula for finding nth
        // decagonal number
        return 4 * n * n - 3 * n;
    }

    // Driver Code
    public static void Main()
    {
        int n = 10;
        Console.Write(n + "th decagonal number : "
                                   + decagonal(n));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find nth
// decagonal number

// Function to calculate
// decagonal number
function decagonal($n)
{

    // Formula for finding nth
    // decagonal number
    return 4 * $n * $n - 3 * $n;
}

// Driver function
$n = 10;
echo $n, "th decagonal number :",
                 decagonal($n);

// This code is contributed by ajit
?>

Javascript

<script>

// JavaScript program for Decagonal Numbers

// Function to calculate
// decagonal number
function decagonal(n)
{

    // Formula for finding nth
    // decagonal number
    return 4 * n * n - 3 * n;
}

// Driver code
let n = 10;
document.write(n + "th decagonal number : " +
               decagonal(n));

// This code is contributed by souravghosh0416

</script>

Output: 

10th decagonal number : 370

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