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++ 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 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 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 |
# 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# 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 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 ?> |
<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