Número tetraédrico centrado

Nos dan el número entero n, necesitamos encontrar el número tetraédrico centrado en el n-ésimo.
Descripción: El número tetraédrico centrado es un número figurado centrado que representa un tetraedro.
Números tetraédricos: un número se denomina número tetraédrico si se puede representar como una pirámide con una base triangular y tres lados, llamada tetraedro. El enésimo número tetraédrico es la suma de los primeros n números triangulares . 
Las primeras series de números tetraédricos centrados son: 
1, 5, 15, 35, 69, 121, 195, 295, 425, 589……………………….
Enésimo término matemático del número tetraédrico centrado:
 

Ejemplos:
 

Input : n = 3
Output : 35

Input : n = 9
Output : 589

A continuación se muestra la implementación de la fórmula anterior. 
 

// C++ Program to find nth
// Centered tetrahedral number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find centered
// 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
// 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
    // 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
    // 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
// 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
// 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>

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