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 functionint 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 Codeint 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 functionint 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 Codeint 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 numberimport java.io.*;class GFG { // centered pentagonal// number functionstatic 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 Codepublic 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 Coden = 7print("%sth Centered pentagonal number : " %n, centered_pentagonal_Num(n)) # This code is contributed by ajit |
C#
// C# Program to find nth// Centered pentagonal numberusing System;class GFG { // centered pentagonal// number functionstatic 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 Codepublic 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 functionfunction 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 functionfunction 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 Codevar 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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