中心五边形数

给定一个整数 n，找出第 n 个中心五边形数。
一个居中的五边形数是一个居中的数字，它表示一个五边形，中心有一个点，其他点依次在五边形层中围绕它[来源：维基]

几个中心五边形数是：
1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391………………..
例子 ：

Input : 3
Output : 16

Input : 9
Output : 181

方法：
第 n项的中心五边形由下式给出：

$Cp_{n}=(5n^2-5n+2)/2$

上述方法的基本实现：

C++

// Program to find nth
// Centered pentagonal number.
#include 
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;
}

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.

Javascript

// 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

输出 ：

7th Centered pentagonal number: 106

时间复杂度： O(1)
辅助空间： O(1)

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