Un número se denomina número tetraédrico si se puede representar como una pirámide con una base triangular y tres lados, llamada tetraedro. El n- ésimo número tetraédrico es la suma de los primeros n números triangulares .
Los diez primeros números tetraédricos son:
1, 4, 10, 20, 35, 56, 84, 120, 165, 220,…
Fórmula para el enésimo número tetraédrico:
Tn = (n * (n + 1) * (n + 2)) / 6
Prueba:
The proof uses the fact that the nth tetrahedral number is given by, Trin = (n * (n + 1)) / 2 It proceeds by induction. Base Case T1 = 1 = 1 * 2 * 3 / 6 Inductive Step Tn+1 = Tn + Trin+1 Tn+1 = [((n * (n + 1) * (n + 2)) / 6] + [((n + 1) * (n + 2)) / 2] Tn+1 = (n * (n + 1) * (n + 2)) / 6
A continuación se muestra la implementación de la idea anterior:
C++
// CPP Program to find the // nth tetrahedral number #include <iostream> using namespace std; int tetrahedralNumber(int n) { return (n * (n + 1) * (n + 2)) / 6; } // Driver Code int main() { int n = 5; cout << tetrahedralNumber(n) << endl; return 0; }
Java
// Java Program to find the // nth tetrahedral number class GFG { // Function to find Tetrahedral Number static int tetrahedralNumber(int n) { return (n * (n + 1) * (n + 2)) / 6; } // Driver Code public static void main(String[] args) { int n = 5; System.out.println(tetrahedralNumber(n)); } } // This code is contributed by Manish Kumar Rai.
Python
# Python3 Program to find the # nth tetrahedral number def tetrahedralNumber(n): return (n * (n + 1) * (n + 2)) / 6 # Driver Code n = 5 print (tetrahedralNumber(n))
C#
// C# Program to find the // nth tetrahedral number using System; public class GFG{ // Function to find Tetrahedral Number static int tetrahedralNumber(int n) { return (n * (n + 1) * (n + 2)) / 6; } // Driver code static public void Main () { int n = 5; Console.WriteLine(tetrahedralNumber(n)); } } // This code is contributed by Ajit.
PHP
<?php // PHP Program to find the // nth tetrahedral number function tetrahedralNumber($n) { return ($n * ($n + 1) * ($n + 2)) / 6; } // Driver Code $n = 5; echo tetrahedralNumber($n); // This code is contributed by mits ?>
Javascript
<script> // JavaScript Program to find the // nth tetrahedral number // Function to find Tetrahedral Number function tetrahedralNumber(n) { return (n * (n + 1) * (n + 2)) / 6; } // Driver code let n = 5; document.write(tetrahedralNumber(n)); // This code is contributed by code_hunt. </script>
Producción:
35
Complejidad temporal : O(1).
Complejidad del espacio : O(1) ya que usa variables constantes
Publicación traducida automáticamente
Artículo escrito por Nishant Tanwar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA