Centered Octahedral number
We are given a number n, we need to find n-th centered octahedral number.
Description: A centered octahedral number is a figurate number. It counts the number of points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases of the Delannoy numbers, which count certain two-dimensional lattice paths.
The First Few Centered octahedral numbers (where n = 0, 1, 2, 3…….) are :
1, 7, 25, 63, 129, 231, 377, 575, 833, 1159………………………….
Mathematics formula for nth Centered octahedral number:
Examples :
Input : n = 6 Output : 377 Input : n = 15 Output : 4991
C++
// C++ Program to find nth // Centered octahedral number #include <bits/stdc++.h> using namespace std; // Function to find // Centered octahedral number int centeredOctahedral( int n) { // Formula to calculate nth // Centered octahedral number // and return it into main function. return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3; } // Driver Code int main() { int n = 3; cout << centeredOctahedral(n) << endl; n = 9; cout << centeredOctahedral(n) << endl; return 0; } |
C
// C Program to find nth // Centered octahedral number #include <stdio.h> // Function to find // Centered octahedral number int centeredOctahedral( int n) { // Formula to calculate nth // Centered octahedral number // and return it into main function. return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3; } // Driver Code int main() { int n = 3; printf ( "%d\n" ,centeredOctahedral(n)); n = 9; printf ( "%d\n" ,centeredOctahedral(n)); return 0; } // This code is contributed by kothavvsaakash. |
Java
// Java Program to find nth // Centered octahedral number import java.io.*; class GFG { // Function to find // Centered octahedral number static int centeredOctahedral( int n) { // Formula to calculate nth // Centered octahedral number // and return it into main function. return ( 2 * n + 1 ) * ( 2 * n * n + 2 * n + 3 ) / 3 ; } // Driver Code public static void main (String[] args) { int n = 3 ; System.out.print( centeredOctahedral(n)); System.out.println(); n = 9 ; System.out.print(centeredOctahedral(n)); } } // This code is contributed by aj_36 |
Python3
# Python 3 Program to find nth # Centered octahedral number # Centered octahedral # number function def centeredOctahedral(n) : # Formula to calculate nth # Centered octahedral number # return it into main function. return ( 2 * n + 1 ) * ( 2 * n * n + 2 * n + 3 ) / / 3 # Driver Code if __name__ = = '__main__' : n = 3 print (centeredOctahedral(n)) n = 9 print (centeredOctahedral(n)) # This code is contributed ajit |
C#
// C# Program to find nth // Centered octahedral number using System; public class GFG { // Function to find // Centered octahedral number static int centeredOctahedral( int n) { // Formula to calculate nth // Centered octahedral number // and return it into main function. return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3; } // Driver Code static public void Main () { int n = 3; Console.WriteLine( centeredOctahedral(n)); n = 9; Console.WriteLine( centeredOctahedral(n)); } } // This code is contributed by m_kit. |
PHP
<?php // PHP Program to find nth // Centered octahedral number // Function to find // Centered octahedral number function centeredOctahedral( $n ) { // Formula to calculate // nth Centered octahedral // number and return it // into main function. return (2 * $n + 1) * (2 * $n * $n + 2 * $n + 3) / 3; } // Driver Code $n = 3; echo centeredOctahedral( $n ), "\n" ; $n = 9; echo centeredOctahedral( $n ), "\n" ; // This code is contributed ajit ?> |
Javascript
<script> // Javascript Program to find nth // Centered octahedral number // Function to find // Centered octahedral number function centeredOctahedral(n) { // Formula to calculate nth // Centered octahedral number // and return it into main function. return (2 * n + 1) * (2 * n * n + 2 * n + 3) / 3; } // Driver Code var n = 3; document.write(centeredOctahedral(n)); document.write( "<br>" ); n = 9; document.write(centeredOctahedral(n)); // This code is contributed by Kirti </script> |
Output :
63 1159
Time Complexity: O(1)
Auxiliary Space: O(1)
Reference:
https://en.wikipedia.org/wiki/Centered_octahedral_number
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