Given an integer n, find the nth Centered pentagonal number.
A Centered Pentagonal Number is a centered figurate number that represents a pentagon with a dot in the center and other dots surrounding it in pentagonal layers successively [ Source: Wiki ]
Few Centered pentagonal Number are :
1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391………………..
Examples :
Input : 3 Output : 16 Input : 9 Output : 181
Approach:
Centered pentagonal for n-th term is given by :
Basic implementation of the above approach :
C++
// Program to find nth // Centered pentagonal number. #include <bits/stdc++.h> using namespace std;
// centered pentagonal number function int centered_pentagonal_Num( int n)
{ // Formula to calculate nth
// Centered pentagonal number
// and return it into main function.
return (5 * n * n - 5 * n + 2) / 2;
} // Driver Code int main()
{ int n = 7;
cout << n << "th Centered pentagonal number: " ;
cout << centered_pentagonal_Num(n);
return 0;
} |
C
// C Program to find nth // Centered pentagonal number. #include <stdio.h> // centered pentagonal number function int centered_pentagonal_Num( int n)
{ // Formula to calculate nth
// Centered pentagonal number
// and return it into main function.
return (5 * n * n - 5 * n + 2) / 2;
} // Driver Code int main()
{ int n = 7;
printf ( "%dth Centered pentagonal number: " ,n);
printf ( "%d" ,centered_pentagonal_Num(n));
return 0;
} // This code is contributed by kothavvsaakash. |
Java
// Program to find nth // Centered pentagonal number import java.io.*;
class GFG
{ // centered pentagonal // number function static int centered_pentagonal_Num( int n)
{ // Formula to calculate
// nth Centered pentagonal
// number and return it
// into main function.
return ( 5 * n * n - 5 * n + 2 ) / 2 ;
} // Driver Code public static void main (String[] args)
{ int n = 7 ;
System.out.print(n + "th Centered " +
"pentagonal number: " );
System.out.println(centered_pentagonal_Num(n)); } } // This code is contributed by anuj_67. |
Python3
# Python program to find Nth # Centered pentagonal number. # Function to calculate # Centered pentagonal number. def centered_pentagonal_Num(n):
# Formula to calculate nth
# Centered pentagonal number.
return ( 5 * n * n - 5 * n + 2 ) / / 2
# Driver Code n = 7
print ( "%sth Centered pentagonal number : " % n,
centered_pentagonal_Num(n))
# This code is contributed by ajit |
C#
// C# Program to find nth // Centered pentagonal number using System;
class GFG
{ // centered pentagonal // number function static int centered_pentagonal_Num( int n)
{ // Formula to calculate
// nth Centered pentagonal
// number and return it
// into main function.
return (5 * n * n - 5 * n + 2) / 2;
} // Driver Code public static void Main ()
{ int n = 7;
Console.Write(n + "th Centered " +
"pentagonal number: " );
Console.WriteLine(centered_pentagonal_Num(n)); } } // This code is contributed by anuj_67. |
PHP
<?php // PHP Program to find nth // Centered pentagonal number. // Centered pentagonal number function function centered_pentagonal_Num( $n )
{ // Formula to calculate nth
// Centered pentagonal number
// and return it into main function.
return (5 * $n * $n - 5 * $n + 2) / 2;
} // Driver Code $n = 7;
echo $n , "th Centered pentagonal number: " ;
echo centered_pentagonal_Num( $n );
// This code is contributed by aj_36 ?> |
Javascript
<script> // Program to find nth // Centered pentagonal number // centered pentagonal // number function function centered_pentagonal_Num(n)
{ // Formula to calculate
// nth Centered pentagonal
// number and return it
// into main function.
return (5 * n * n - 5 * n + 2) / 2;
} // Driver Code var n = 7;
document.write(n + "th Centered " +
"pentagonal number: " );
document.write(centered_pentagonal_Num(n)); // This code is contributed by Amit Katiyar </script> |
Output :
7th Centered pentagonal number: 106
Time Complexity: O(1)
Auxiliary Space: O(1)
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