Centered Octagonal Number
Given a number n, find the nth centered octagonal number.
A centered octagonal number represents an octagon with a dot in the center and others dots surrounding the center dot in the successive octagonal layer.
Examples :
Input : 2 Output : 9 Input : 5 Output : 81
Centered Octagonal n-th Number is given by :
Basic Implementation of the above approach:
C++
// Program to find nth // centered octagonal // number #include <bits/stdc++.h> using namespace std; // Centered octagonal number function int cen_octagonalnum( long int n) { // Formula to calculate nth // centered octagonal number & // return it into main function. return (4 * n * n - 4 * n + 1); } // Driver Code int main() { long int n = 6; cout << n << "th centered" << " octagonal number : " ; cout << cen_octagonalnum(n); cout << endl; n = 11; cout << n << "th centered" << " octagonal number : " ; cout << cen_octagonalnum(n); return 0; } |
C
// C Program to find nth // centered octagonal // number #include <stdio.h> // Centered octagonal number function int cen_octagonalnum( long int n) { // Formula to calculate nth // centered octagonal number & // return it into main function. return (4 * n * n - 4 * n + 1); } // Driver Code int main() { long int n = 6; printf ( "%ldth centered octagonal number : " ,n); printf ( "%d\n" ,cen_octagonalnum(n)); n = 11; printf ( "%ldth centered octagonal number : " ,n); printf ( "%d\n" ,cen_octagonalnum(n)); return 0; } // This code is contributed by kothavvsaakash. |
Java
// Java Program to find nth // centered octagonal number import java.io.*; class GFG { // Function to find centered // octagonal number static int centeredoctagonalNumber( int n) { // Formula to calculate nth // centered octagonal number // and return it into main function return 4 * n * (n - 1 ) + 1 ; } // Driver Code public static void main(String args[]) { int n = 6 ; System.out.print(n + "th centered " + "octagonal number: " ); System.out.println( centeredoctagonalNumber(n)); n = 11 ; System.out.print(n + "th centered " + "octagonal number: " ); System.out.println( centeredoctagonalNumber(n)); } } // This code has been contributed by Prasad_Kshirsagar. |
Python3
# Program to find nth # centered octagonal number def cen_octagonalnum(n) : # Formula to calculate nth # centered octagonal number return ( 4 * n * n - 4 * n + 1 ) # Driver Code if __name__ = = '__main__' : n = 6 print (n, "th Centered" , "octagonal number: " , cen_octagonalnum(n)) n = 11 print (n, "th Centered" , "octagonal number: " , cen_octagonalnum(n)) # This code is contributed # by akt_mit |
C#
// Program to find nth centered octagonal // number using System; public class GFG{ // Centered octagonal number function static long cen_octagonalnum( long n) { // Formula to calculate nth // centered octagonal number & // return it into main function. return (4 * n * n - 4 * n + 1); } // Driver code static public void Main () { long n = 6; Console.WriteLine(n + "th centered" + " octagonal number : " + cen_octagonalnum(n)); n = 11; Console.WriteLine(n + "th centered" + " octagonal number : " + cen_octagonalnum(n)); } } // This code is contributed by anuj_67. |
PHP
<?php // Program to find nth // centered octagonal // number // Centered octagonal // number function function cen_octagonalnum( $n ) { // Formula to calculate nth // centered octagonal number & // return it into main function. return (4 * $n * $n - 4 * $n + 1); } // Driver Code $n = 6; echo $n , "th centered" , " octagonal number : " ; echo cen_octagonalnum( $n ); echo "\n" ; $n = 11; echo $n , "th centered" , " octagonal number : " ; echo cen_octagonalnum( $n ); // This code is contributed by ajit ?> |
Javascript
<script> // Javascript Program to find nth // centered octagonal number // Function to find centered // octagonal number function centeredoctagonalNumber(n) { // Formula to calculate nth // centered octagonal number // and return it into main function return 4 * n * (n - 1) + 1; } // Driver Code var n = 6; document.write(n + "th centered " + "octagonal number: " ); document.write(centeredoctagonalNumber(n) + "<br>" ); n = 11; document.write(n + "th centered " + "octagonal number: " ); document.write(centeredoctagonalNumber(n)); // This code is contributed by Kirti </script> |
Output
6th centered octagonal number : 121 11th centered octagonal number : 441
Time Complexity: O(1)
Auxiliary Space: O(1)
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