We are given integer n, we need to find n-th centered tetrahedral number.
Description: The centered tetrahedral number is a centered figurate number that represents a tetrahedron.
Tetrahedral Numbers: A number is termed as a tetrahedral number if it can be represented as a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number is the sum of the first n triangular numbers.
The first few centered tetrahedral number series are:
1, 5, 15, 35, 69, 121, 195, 295, 425, 589……………………….
Mathematical nth Term of centered tetrahedral number:
Examples :
Input : n = 3 Output : 35 Input : n = 9 Output : 589
Below is the implementation of above formula.
// C++ Program to find nth // Centered tetrahedral number #include <bits/stdc++.h> using namespace std;
// Function to find // Centered tetrahedral number int centeredTetrahedralNumber( int n)
{ // Formula to calculate nth
// Centered tetrahedral number
// and return it into main function.
return (2 * n + 1) * (n * n + n + 3) / 3;
} // Driver Code int main()
{ int n = 6;
cout << centeredTetrahedralNumber(n);
return 0;
} |
// C Program to find nth // Centered tetrahedral number #include <stdio.h> // Function to find // Centered tetrahedral number int centeredTetrahedralNumber( int n)
{ // Formula to calculate nth
// Centered tetrahedral number
// and return it into main function.
return (2 * n + 1) * (n * n + n + 3) / 3;
} // Driver Code int main()
{ int n = 6;
printf ( "%d" ,centeredTetrahedralNumber(n));
return 0;
} // This code is contributed by kothavvsaakash. |
// Java Program to find nth Centered // tetrahedral number import java.io.*;
class GFG {
// Function to find
// Centered tetrahedral number
static int centeredTetrahedralNumber( int n)
{
// Formula to calculate nth
// Centered tetrahedral number
// and return it into main function.
return ( 2 * n + 1 ) * (n * n + n + 3 ) / 3 ;
}
// Driver Code
public static void main (String[] args)
{
int n = 6 ;
System.out.println(
centeredTetrahedralNumber(n));
}
} // This code is contributed by anuj_67. |
# Python program to find nth # Centered tetrahedral number # Function to calculate # Centered tetrahedral number def centeredTetrahedralNumber(n):
# Formula to calculate nth
# Centered tetrahedral number
# and return it into main function
return ( 2 * n + 1 ) * (n * n + n + 3 ) / / 3
# Driver Code n = 6
print (centeredTetrahedralNumber(n))
# This code is contributed by ajit |
// C# Program to find nth Centered // tetrahedral number using System;
class GFG {
// Function to find
// Centered tetrahedral number
static int centeredTetrahedralNumber( int n)
{
// Formula to calculate nth
// Centered tetrahedral number
// and return it into main function.
return (2 * n + 1) * (n * n + n + 3) / 3;
}
// Driver Code
public static void Main ()
{
int n = 6;
Console.WriteLine(
centeredTetrahedralNumber(n));
}
} // This code is contributed by anuj_67. |
<?php // PHP Program to find nth // Centered tetrahedral number // Function to find // Centered tetrahedral number function centeredTetrahedralNumber( $n )
{ // Formula to calculate nth
// Centered tetrahedral number
// and return it into main function.
return (2 * $n + 1) *
( $n * $n + $n + 3) / 3;
} // Driver Code $n = 6;
echo centeredTetrahedralNumber( $n );
// This code is contributed by anuj_67. ?> |
<script> // Javascript program to find nth Centered // tetrahedral number // Function to find // Centered tetrahedral number function centeredTetrahedralNumber(n)
{ // Formula to calculate nth
// Centered tetrahedral number
// and return it into main function.
return (2 * n + 1) * (n * n + n + 3) / 3;
} // Driver Code // Given Number var n = 6;
document.write(centeredTetrahedralNumber(n)); // This code is contributed by Kirti </script> |
Output :
195
Time Complexity: O(1)
Auxiliary Space: O(1)