requisitos previos:
Dado un valor n, la tarea es imprimir series de números tetraédricos hasta el término n.
Ejemplos:
Input: 5 Output: 1 4 10 20 35 Input: 10 Output: 1 4 10 20 35 56 84 120 165 220
Método 1: Uso de series de números triangulares:
este problema se puede resolver fácilmente con el hecho de que el N número tetraédrico es igual a la suma de los primeros N números triangulares.
Echemos un vistazo a las series de números triangulares y tetraédricos.
To print series upto 5th term:
Triangular Numbers = 1 3 6 10 15
Tetrahedral numbers = 1 4 10 20 35
i.e (1) (1 + 3) (1 + 3 + 6) (1 + 3 + 6 + 10) (1 + 3 + 6 + 10 + 35)
Calcule el N número triangular usando la fórmula 
Entonces, imprima la serie de números tetraédricos generando números triangulares y sumándolos con la suma de todos los números triangulares generados previamente.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ program to generate tetrahedral
// number series
#include <bits/stdc++.h>
using namespace std;
// function to generate nth triangular
// number
long findTriangularNumber(int n)
{
return (n * (n + 1)) / 2;
}
// function to print tetrahedral number
// series up to n
void printSeries(int n)
{
// Initialize prev as 0. It stores
// the sum of all previously generated
// triangular number
int prev = 0;
int curr;
// Loop to print series
for (int i = 1; i <= n; i++)
{
// Find ith triangular number
curr = findTriangularNumber(i);
// Add ith triangular number to
// sum of all previously generated
// triangular number to get ith
// tetrahedral number
curr = curr + prev;
cout << curr << " ";
// Update sum of all previously
// generated triangular number
prev = curr;
}
}
// Driver code
int main()
{
int n = 10;
// function call to print series
printSeries(n);
return 0;
}
Java
// Java program to generate tetrahedral
// number series
import java.io.*;
class GFG {
// function to generate nth triangular
// number
static long findTriangularNumber(int n)
{
return (n * (n + 1)) / 2;
}
// function to print tetrahedral number
// series up to n
static void printSeries(int n)
{
// Initialize prev as 0. It store
// the sum of all previously generated
// triangular number
long prev = 0;
long curr;
// Loop to print series
for (int i = 1; i <= n; i++)
{
// Find ithh triangular number
curr = findTriangularNumber(i);
// Add ith triangular number to
// sum of all previously generated
// triangular number to get ith
// tetrahedral number
curr = curr + prev;
System.out.print(curr + " ");
// Update sum of all previously
// generated triangular number
prev = curr;
}
}
// Driver code
public static void main (String[] args)
{
int n = 10;
// function call to print series
printSeries(n);
}
}
Python3
# Python3 program to generate # tetrahedral number series # function to generate nth # triangular number def findTriangularNumber(n): return (n * (n + 1)) / 2 # function to print tetrahedral # number series up to n def printSeries(n): # Initialize prev as 0. # It stores the sum of all # previously generated # triangular number prev = 0 # Loop to print series for i in range(1, n+1): # Find ith triangular number curr = findTriangularNumber(i) # Add ith triangular number # to sum of all previously # generated triangular number # to get ith tetrahedral number curr = int(curr + prev) print(curr, end = ' ') # Update sum of all previously # generated triangular number prev = curr # Driver code n = 10 # function call to # print series printSeries(n) # This code is contributed by Mahadev.
C#
// C# program to generate tetrahedral
// number series
using System;
public class GFG{
// function to generate nth triangular
// number
static long findTriangularNumber(int n)
{
return (n * (n + 1)) / 2;
}
// function to print tetrahedral number
// series up to n
static void printSeries(int n)
{
// Initialize prev as 0. It store
// the sum of all previously generated
// triangular number
long prev = 0;
long curr;
// Loop to print series
for (int i = 1; i <= n; i++)
{
// Find ithh triangular number
curr = findTriangularNumber(i);
// Add ith triangular number to
// sum of all previously generated
// triangular number to get ith
// tetrahedral number
curr = curr + prev;
Console.Write(curr + " ");
// Update sum of all previously
// generated triangular number
prev = curr;
}
}
// Driver code
static public void Main ()
{
int n = 10;
// function call to print series
printSeries(n);
}
}
PHP
<?php
// PHP program to generate tetrahedral
// number series
// function to generate nth triangular
// number
function findTriangularNumber($n)
{
return ($n * ($n + 1)) / 2;
}
// function to print tetrahedral number
// series up to n
function printSeries($n)
{
// Initialize prev as 0. It store
// the sum of all previously generated
// triangular number
$prev = 0;
$curr;
// Loop to print series
for ($i = 1; $i <= $n; $i++)
{
// Find ithh triangular number
$curr = findTriangularNumber($i);
// Add ith triangular number to
// sum of all previously generated
// triangular number to get ith
// tetrahedral number
$curr = $curr + $prev;
echo($curr . " ");
// Update sum of all previously
// generated triangular number
$prev = $curr;
}
}
// Driver code
$n = 10;
// function call to print series
printSeries($n);
?>
Javascript
<script>
// Javascript program to generate tetrahedral
// number series
// function to generate nth triangular
// number
function findTriangularNumber(n)
{
return (n * (n + 1)) / 2;
}
// function to print tetrahedral number
// series up to n
function printSeries(n)
{
// Initialize prev as 0. It stores
// the sum of all previously generated
// triangular number
var prev = 0;
var curr;
// Loop to print series
for (var i = 1; i <= n; i++)
{
// Find ith triangular number
curr = findTriangularNumber(i);
// Add ith triangular number to
// sum of all previously generated
// triangular number to get ith
// tetrahedral number
curr = curr + prev;
document.write( curr + " ");
// Update sum of all previously
// generated triangular number
prev = curr;
}
}
// Driver code
var n = 10;
// function call to print series
printSeries(n);
// This code is contributed by itsok.
</script>
Producción:
1 4 10 20 35 56 84 120 165 220
Complejidad de tiempo: O(n), donde n representa el entero dado.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.
Método 2: uso de la fórmula del número tetraédrico:
fórmula para encontrar el número tetraédrico n- ésimo : 
a continuación se muestra la implementación requerida:
C++
// C++ program to generate series of
// tetrahedral numbers
#include <bits/stdc++.h>
using namespace std;
// function to print tetrahedral
// number series up to n
void printSeries(int n)
{
// loop to print series
for (int i = 1; i <= n; i++)
{
// Calculate and print ith
// tetrahedral number
int num = i * (i + 1) * (i + 2) / 6;
cout << num << " ";
}
}
// Driver code
int main()
{
int n = 10;
// function call to print series
printSeries(n);
return 0;
}
Java
// Java program to generate series of
// tetrahedral numbers
import java.io.*;
class GFG {
// function to print tetrahedral
// number series up to n
static void printSeries(int n)
{
// loop to print series
for (int i = 1; i <= n; i++)
{
// Calculate and print ith
// tetrahedral number
int num = i * (i + 1) * (i + 2) / 6;
System.out.print(num + " ");
}
}
// Driver code
public static void main (String[] args)
{
int n = 10;
// function call to print series
printSeries(n);
}
}
Python3
# Python3 code to print tetrahedral # numbers series up to n # function to print tetrahedral series up to n def printSeries(n): # loop to print series for i in range(1, n + 1): # Calculate and print ith # Tetrahedral number num = i * (i + 1) * (i + 2) // 6 print(num, end =' ') # Driver code n = 10 # function call to print series printSeries(n)
C#
// C# program to generate series of
// tetrahedral numbers
using System;
public class GFG{
// function to print tetrahedral
// number series up to n
static void printSeries(int n)
{
// loop to print series
for (int i = 1; i <= n; i++)
{
// Calculate and print ith
// tetrahedral number
int num = i * (i + 1) * (i + 2) / 6;
Console.Write(num + " ");
}
}
// Driver code
static public void Main ()
{
int n = 10;
// function call to print series
printSeries(n);
}
}
PHP
<?php
// PHP program to generate series of
// tetrahedral numbers
// function to print tetrahedral
// number series up to n
function printSeries($n)
{
// loop to print series
for ($i = 1; $i <= $n; $i++)
{
// Calculate and print ith
// tetrahedral number
$num = $i * ($i + 1) * ($i + 2) / 6;
echo ($num . " ");
}
}
// Driver code
$n = 10;
// function call to print series
printSeries($n);
?>
Javascript
<script>
// Javascript program to generate series of
// tetrahedral numbers
// function to print tetrahedral
// number series up to n
function printSeries(n)
{
let i;
// loop to print series
for (i = 1; i <= n; i++)
{
// Calculate and print ith
// tetrahedral number
let num = i * (i + 1) * ((i + 2) / 6);
document.write(num + " ");
}
}
// driver program
let n = 10;
// function call to print series
printSeries(n);
// This code is contributed by susmitakundugoaldanga.
</script>
Producción:
1 4 10 20 35 56 84 120 165 220
Complejidad de tiempo: O(n), donde n representa el entero dado.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.