Given a number n, find the nth Centered Hexadecagonal Number.
A Centered Hexadecagonal number represents a dot in the center and other dots around it in successive hexadecagonal(16 sided polygon) layers.
The first few Centered Hexadecagonal numbers are:
1, 17, 49, 97, 161, 241, 337, 449, 577, 721, 881………………….
Examples :
Input : 3 Output : 49 Input : 10 Output : 721
In mathematics, Centered hexadecagonal number for the n-th term is given by :
Below is the basic implementation of the above idea:
C++
// C++ Program to find// nth centered hexadecagonal// number#include <bits/stdc++.h>using namespace std;// centered hexadecagonal functionint center_hexadecagonal_num(long int n){ // Formula to calculate nth // centered hexadecagonal number return 8 * n * n - 8 * n + 1;}// Driver Codeint main(){ long int n = 2; cout << n << "th centered hexadecagonal number : " << center_hexadecagonal_num(n); cout << endl; n = 12; cout << n << "th centered hexadecagonal number : " << center_hexadecagonal_num(n); return 0;} |
C
// C Program to find// nth centered hexadecagonal// number#include <stdio.h>// centered hexadecagonal functionint center_hexadecagonal_num(long int n){ // Formula to calculate nth // centered hexadecagonal number return 8 * n * n - 8 * n + 1;}// Driver Codeint main(){ long int n = 2; printf("%ldth centered hexadecagonal number : %d\n",n,center_hexadecagonal_num(n)); n = 12; printf("%ldth centered hexadecagonal number : %d\n",n,center_hexadecagonal_num(n)); return 0;}// This code is contributed by kothavvsaakash. |
Java
// Java Program to find nth// centered hexadecagonal numberimport java.io.*;class GFG { // centered hexadecagonal function static int center_hexadecagonal_num(int n) { // Formula to calculate nth // centered hexadecagonal number return 8 * n * n - 8 * n + 1; } // Driver Code public static void main(String args[]) { int n = 2; System.out.print(n + "th centered " + "hexadecagonal number: "); System.out.println(center_hexadecagonal_num(n)); n = 12; System.out.print(n + "th centered " + "hexadecagonal number: "); System.out.println(center_hexadecagonal_num(n)); }}// This code is contributed by ajit. |
Python3
# Program to find nth # centered hexadecagonal # number# centered hexadecagonal # functiondef center_hexadecagonal_num(n): # Formula to calculate # nth centered hexadecagonal # number return 8 * n * n - 8 * n + 1# Driver Codeif __name__ == '__main__' : n = 2 print(n,"nd centered hexadecagonal " + "number : ", center_hexadecagonal_num(n)) n = 12 print(n,"th centered hexadecagonal " + "number : ", center_hexadecagonal_num(n)) # This code is contributed# by akt_mit |
C#
// C# Program to find nth// centered hexadecagonal numberusing System;class GFG{ // centered hexadecagonal // function static int center_hexadecagonal_num(int n) { // Formula to calculate nth // centered hexadecagonal number return 8 * n * n - 8 * n + 1; } // Driver Code static public void Main () { int n = 2; Console.Write(n + "th centered " + "hexadecagonal number: "); Console.WriteLine(center_hexadecagonal_num(n)); n = 12; Console.Write(n + "th centered " + "hexadecagonal number: "); Console.WriteLine(center_hexadecagonal_num(n)); }}// This code is contributed by m_kit |
PHP
<?php// PHP Program to find// nth centered hexadecagonal// number// centered hexadecagonal functionfunction center_hexadecagonal_num($n){ // Formula to calculate nth // centered hexadecagonal number return 8 * $n * $n - 8 * $n + 1;}// Driver Code$n = 2;echo $n , "th centered hexadecagonal number : ", center_hexadecagonal_num($n);echo "\n";$n = 12;echo $n , "th centered hexadecagonal numbe : ", center_hexadecagonal_num($n);// This code is contributed by ajit?> |
Javascript
<script>// Javascript Program to find nth// centered hexadecagonal number// Centered hexadecagonal functionfunction center_hexadecagonal_num(n){ // Formula to calculate nth // centered hexadecagonal number return 8 * n * n - 8 * n + 1;}// Driver codevar n = 2;document.write(n + "th centered " + "hexadecagonal number: ");document.write(center_hexadecagonal_num(n) + "<br>");n = 12;document.write(n + "th centered " + "hexadecagonal number: ");document.write(center_hexadecagonal_num(n));// This code is contributed by Ankita saini</script> |
Output :
2nd centered hexadecagonal number : 17 12th centered hexadecagonal number : 1057
Time Complexity: O(1)
Auxiliary Space: O(1)
References:
http://oeis.org/A069129
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