Centered decagonal number

Last Updated : 19 May, 2022

Given a number n, find the nth Centered decagonal number .
A Centered Decagonal Number is centered figurative number that represents a decagon with dot in center and all other dot surrounding it in successive decagonal form. Source[Wiki].

Center Decagonal number

The first few Centered Decagonal Numbers are :
1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661............
Examples :

Input :  3
Output : 31

Input : 6
Output : 151

In mathematics centered decagonal number for n-th term is given by :

Cd_{n}= 5n^2+5n+1

Below is the basic implementation of the above idea.

C++

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

// Centered decagonal
// number function

int centereddecagonalnum(int n)
{
    // Formula to calculate nth
    // centered decagonal number &
    // return it into main function.
    return (5 * n * n + 5 * n + 1);
}

// Driver Code
int main()
{
    int n = 5;
    cout << n << "th centered decagonal"
                          << "number: ";
    cout << centereddecagonalnum(n);
    cout << endl;
    n = 9;
    cout << n << "th centered decagonal"
                          << "number: ";
    cout << centereddecagonalnum(n);

    return 0;
}

// C Program to find nth
// centered decagonal 
// number
#include <stdio.h>

// Centered decagonal
// number function

int centereddecagonalnum(int n)
{
    // Formula to calculate nth
    // centered decagonal number &
    // return it into main function.
    return (5 * n * n + 5 * n + 1);
}

// Driver Code
int main()
{
    int n = 5;
    printf("%dth centered decagonal number: ",n);
    printf("%d\n",centereddecagonalnum(n));

    n = 9;
    printf("%dth centered decagonal number: ",n);
    printf("%d\n",centereddecagonalnum(n));

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java Program to find nth
// centered decagonal number
import java.io.*;

class GFG 
{
    
    // Centered decagonal
    // number function
    static int centereddecagonalnum(int n)
    {
        
    // Formula to calculate nth
    // centered decagonal number &
    // return it into main function.
    return (5 * n * n + 5 * n + 1);
    }

    // Driver Code
    public static void main (String[] args) 
    {
        int n = 5;
        System.out.print(n + "th centered " + 
                       "decagonal number: ");
        System.out.println(centereddecagonalnum(n));

        n = 9;
        System.out.print(n + "th centered " + 
                       "decagonal number: ");
        System.out.println(centereddecagonalnum(n));
    }
}

// This code is contributed by m_kit

Python3

# Program to find nth
# centered decagonal number

# Centered decagonal
# number function
def centereddecagonalnum(n) :
    
    # Formula to calculate 
    # nth centered decagonal 
    # number & return it
    # into main function.
    return (5 * n * n + 
            5 * n + 1)

# Driver Code
if __name__ == '__main__' :
        
    n = 5
    print(n,"th centered decagonal " +
                          "number : ", 
              centereddecagonalnum(n))

    n = 9
    print(n,"th centered decagonal " +
                          "number : ", 
              centereddecagonalnum(n))
              
# This code is contributed by m_kit

// Program to find nth
// centered decagonal 
// number
using System;

class GFG
{
// Centered decagonal
// number function
static int centereddecagonalnum(int n)
{
    // Formula to calculate nth
    // centered decagonal number &
    // return it into main function.
    return (5 * n * n + 5 * n + 1);
}

// Driver Code
static public void Main ()
{
int n = 5;
Console.Write(n + "th centered decagonal"+
                              "number: ");
Console.WriteLine(centereddecagonalnum(n));

n = 9;
Console.Write(n + "th centered decagonal"+
                              "number: ");
Console.WriteLine(centereddecagonalnum(n));
}
}

// This code is contributed by aj_36

PHP

<?php
// Program to find nth
// centered decagonal number

// Centered decagonal
// number function
function centereddecagonalnum($n)
{
    // Formula to calculate 
    // nth centered decagonal 
    // number & return it 
    // into main function.
    return (5 * $n * $n + 
            5 * $n + 1);
}

// Driver Code
$n = 5;
echo $n , "th centered decagonal",
                       "number: ";
echo centereddecagonalnum($n);
echo "\n";

$n = 9;
echo $n , "th centered decagonal",
                       "number: ";
echo centereddecagonalnum($n);

// This code is contributed by ajit
?>

JavaScript

<script>

// Javascript Program to find nth
// centered decagonal number

// Centered decagonal
// number function
function centereddecagonalnum(n)
{
    
    // Formula to calculate nth
    // centered decagonal number &
    // return it into main function.
    return (5 * n * n + 5 * n + 1);
}

// Driver Code 
var n = 5;
document.write(n + "th centered " + 
               "decagonal number: ");
document.write(centereddecagonalnum(n) + "<br>");

n = 9;
document.write(n + "th centered " + 
               "decagonal number: ");
document.write(centereddecagonalnum(n));

// This code is contributed by Kirti
    
</script>

Output

5th centered decagonalnumber: 151
9th centered decagonalnumber: 451

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

Centered Dodecagonal Number

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