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].
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 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
# 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
// 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
?>
<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)
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