Dado un entero n, encuentra el n-ésimo número pentagonal centrado.
Un número pentagonal centrado es un número figurado centrado que representa un pentágono con un punto en el centro y otros puntos rodeándolo en capas pentagonales sucesivamente [Fuente: Wiki ]
Pocos números pentagonales centrados son:
1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391………………..
Ejemplos:
Input : 3 Output : 16 Input : 9 Output : 181
Enfoque:
El pentagonal centrado para el n-ésimo término viene dado por:
Implementación básica del enfoque anterior:
C++
// Program to find nth
// Centered pentagonal number.
#include <bits/stdc++.h>
using namespace std;
// centered pentagonal number function
int centered_pentagonal_Num(int n)
{
// Formula to calculate nth
// Centered pentagonal number
// and return it into main function.
return (5 * n * n - 5 * n + 2) / 2;
}
// Driver Code
int main()
{
int n = 7;
cout << n << "th Centered pentagonal number: ";
cout << centered_pentagonal_Num(n);
return 0;
}
C
// C Program to find nth
// Centered pentagonal number.
#include <stdio.h>
// centered pentagonal number function
int centered_pentagonal_Num(int n)
{
// Formula to calculate nth
// Centered pentagonal number
// and return it into main function.
return (5 * n * n - 5 * n + 2) / 2;
}
// Driver Code
int main()
{
int n = 7;
printf("%dth Centered pentagonal number: ",n);
printf("%d",centered_pentagonal_Num(n));
return 0;
}
// This code is contributed by kothavvsaakash.
Java
// Program to find nth
// Centered pentagonal number
import java.io.*;
class GFG
{
// centered pentagonal
// number function
static int centered_pentagonal_Num(int n)
{
// Formula to calculate
// nth Centered pentagonal
// number and return it
// into main function.
return (5 * n * n - 5 * n + 2) / 2;
}
// Driver Code
public static void main (String[] args)
{
int n = 7;
System.out.print(n + "th Centered " +
"pentagonal number: ");
System.out.println(centered_pentagonal_Num(n));
}
}
// This code is contributed by anuj_67.
Python3
# Python program to find Nth
# Centered pentagonal number.
# Function to calculate
# Centered pentagonal number.
def centered_pentagonal_Num(n):
# Formula to calculate nth
# Centered pentagonal number.
return (5 * n * n - 5 * n + 2) // 2
# Driver Code
n = 7
print("%sth Centered pentagonal number : " %n,
centered_pentagonal_Num(n))
# This code is contributed by ajit
C#
// C# Program to find nth
// Centered pentagonal number
using System;
class GFG
{
// centered pentagonal
// number function
static int centered_pentagonal_Num(int n)
{
// Formula to calculate
// nth Centered pentagonal
// number and return it
// into main function.
return (5 * n * n - 5 * n + 2) / 2;
}
// Driver Code
public static void Main ()
{
int n = 7;
Console.Write(n + "th Centered " +
"pentagonal number: ");
Console.WriteLine(centered_pentagonal_Num(n));
}
}
// This code is contributed by anuj_67.
PHP
<?php
// PHP Program to find nth
// Centered pentagonal number.
// Centered pentagonal number function
function centered_pentagonal_Num($n)
{
// Formula to calculate nth
// Centered pentagonal number
// and return it into main function.
return (5 * $n * $n - 5 * $n + 2) / 2;
}
// Driver Code
$n = 7;
echo $n , "th Centered pentagonal number: ";
echo centered_pentagonal_Num($n);
// This code is contributed by aj_36
?>
Javascript
<script>
// Program to find nth
// Centered pentagonal number
// centered pentagonal
// number function
function centered_pentagonal_Num(n)
{
// Formula to calculate
// nth Centered pentagonal
// number and return it
// into main function.
return (5 * n * n - 5 * n + 2) / 2;
}
// Driver Code
var n = 7;
document.write(n + "th Centered " +
"pentagonal number: ");
document.write(centered_pentagonal_Num(n));
// This code is contributed by Amit Katiyar
</script>
Producción :
7th Centered pentagonal number: 106
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)