Centered tetrahedral number

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++

// 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

// 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

// 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.

Python3

# 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#

// 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
// 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.
?>

Javascript

<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)