número de pentatopo – Part 1

Dado un número n, la tarea es escribir un programa para encontrar el enésimo número de pentátopo. Un número de pentátopo es una clase de número figurativo y se puede representar como patrones geométricos regulares y discretos. En el triángulo pascal, el número en la quinta celda de cualquier fila que comience con el quinto término fila 1 4 6 4 1 de derecha a izquierda o de izquierda a derecha es el número del pentátopo .
Ejemplos: 
 

Entrada: 5 
Salida: 70
Entrada: 8 
Salida: 1001 
 

Los primeros números del pentátopo son: 
1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001………
Fórmula para el enésimo número del pentátopo: 
 

// C++ Program to find the
// nth Pentatope Number
#include <bits/stdc++.h>
using namespace std;
 
// Function that returns nth
// pentatope number
int pentatopeNum(int n)
{
    return (n * (n + 1) * (n + 2) * (n + 3)) / 24;
}
 
// Drivers Code
int main()
{
    // For 5th PentaTope Number
    int n = 5;
    cout << pentatopeNum(n) << endl;
 
    // For 11th PentaTope Number
    n = 11;
    cout << pentatopeNum(n) << endl;
 
    return 0;
}

// C Program to find the
// nth Pentatope Number
#include <stdio.h>
 
// Function that returns nth
// pentatope number
int pentatopeNum(int n)
{
    return (n * (n + 1) * (n + 2) * (n + 3)) / 24;
}
 
// Drivers Code
int main()
{
   
    // For 5th PentaTope Number
    int n = 5;
    printf("%d\n",pentatopeNum(n));
 
    // For 11th PentaTope Number
    n = 11;
    printf("%d\n",pentatopeNum(n));
 
    return 0;
}
 
// This code is contributed by kothavvsaakash.

// Java Program to find the
// nth Pentatope Number
import java.io.*;
 
class GFG
{
     
// Function that returns nth
// pentatope number
static int pentatopeNum(int n)
{
    return (n * (n + 1) *
           (n + 2) * (n + 3)) / 24;
}
// Driver Code
public static void main (String[] args)
{
// For 5th PentaTope Number
int n = 5;
System.out.println(pentatopeNum(n));
 
// For 11th PentaTope Number
n = 11;
System.out.println(pentatopeNum(n));
 
}
}
 
// This code is contributed by m_kit

# Python3 program to find
# nth Pentatope number
 
# Function to calculate
# Pentatope number
def pentatopeNum(n):
 
    # Formula to calculate nth
    # Pentatope number
    return (n * (n + 1) *
                (n + 2) *
                (n + 3) // 24)
 
# Driver Code
n = 5
print(pentatopeNum(n))
n = 11
print(pentatopeNum(n))
 
# This code is contributed
# by ajit.

// C# Program to find the
// nth Pentatope Number
using System;
 
class GFG
{
     
// Function that returns
// nth pentatope number
static int pentatopeNum(int n)
{
    return (n * (n + 1) *
           (n + 2) * (n + 3)) / 24;
}
 
// Driver Code
static public void Main(String []args)
{
     
// For 5th PentaTope Number
int n = 5;
 
Console.WriteLine(pentatopeNum(n));
 
// For 11th PentaTope Number
n = 11;
 
Console.WriteLine(pentatopeNum(n));
}
}
// This code is contributed by Arnab Kundu

<?php
// PHP Program to find the
// nth Pentatope Number
 
// Function that returns
// nth pentatope number
function pentatopeNum($n)
{
    return ($n * ($n + 1) *
                 ($n + 2) *
                 ($n + 3)) / 24;
}
 
// Driver Code
 
// For 5th PentaTope Number
$n = 5;
echo pentatopeNum($n), "\n";
 
// For 11th PentaTope Number
$n = 11;
echo pentatopeNum($n), "\n" ;
 
// This code is contributed
// by aj_36
?>

<script>
 
// Javascript  Program to find the
// nth Pentatope Number
 
// Function that returns
// nth pentatope number
function pentatopeNum(n)
{
    return (n * (n + 1) *
                (n + 2) *
                (n + 3)) / 24;
}
 
// Driver Code
 
// For 5th PentaTope Number
let n = 5;
document.write( pentatopeNum(n)+"<br>");
 
// For 11th PentaTope Number
n = 11;
document.write( pentatopeNum(n));
         
// This code is contributed by sravan kumar
 
</script>

70
1001

Complejidad de tiempo: O(1)
Espacio auxiliar: O(1)
Referencia: https://en.wikipedia.org/wiki/Pentatope_number