中心三角数

给定整数n，找到第n个中心三角数。
中心三角数是一个中心多边形数，代表一个三角形，中间带有一个点，而在相邻的三角形层中，所有其他围绕该中心的点[Source：Wiki]
绘画作品：

前几个居中的三角数系列是：
1，4，10，19，31，46，64，85，109，136，166，199，235，274，316，361，409，460 ………..
例子：

Input : n = 1
Output : 4
Explanation :
A dot in the centre and 3 dots forming the
triangle outside it, thus 4.

Input : n = 6 
Output : 64

Input : n = 10
Output : 166

方法
中心三角数的第n个项由下式给出：

$CT_{n}=(3n^2+3n+2)/2$

上述方法的基本实现：

C++

// CPP Program to find the
// nth Centered Trigunal number
#include
using namespace std;
 
// function for Centered
// Trigunal number
int Centered_Trigunal_num(int n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * n * n + 3 * n + 2) / 2;
}
 
// Driver Code
int main()
{
    // For 3rd Centered Trigunal number
    int n = 3;
    cout << Centered_Trigunal_num(n) << endl;
 
    // For 12th Centered Trigunal number
    n = 12;
    cout << Centered_Trigunal_num(n) << endl;
 
    return 0;
}

Java

// Java Program to find
// the nth Centered
// Triangular number
import java.io.*;
 
class GFG
{
     
// function for Centered
// Trigunal number
static int Centered_Trigunal_num(int n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * n * n +
            3 * n + 2) / 2;
}
 
// Driver Code
public static void main (String[] args)
{
 
// For 3rd Centered
// Trigunal number
int n = 3;
System.out.println(Centered_Trigunal_num(n));
 
// For 12th Centered
// Trigunal number
n = 12;
System.out.println(Centered_Trigunal_num(n));
}
}
 
// This code is contributed by ajit

Python3

# Program to find nth
# Centered Trigunal number
 
def Centered_Trigunal_num(n) :
     
    # Formula to calculate nth
    # Centered Trigunal number
    return (3 * n * n +
            3 * n + 2) // 2
 
# Driver Code
if __name__ == '__main__' :
 
    # For 3rd Centered
    # Trigunal number    
    n = 3
    print(Centered_Trigunal_num(n))
     
    # For 12th Centered
    # Trigunal number
    n = 12
    print(Centered_Trigunal_num(n))
                 
                 
# This code is contributed
# by akt_mit

C#

// C# Program to find
// the nth Centered
// Triangular number
using System;
 
class GFG
{
 
// function for Centered
// Trigunal number
static int Centered_Trigunal_num(int n)
{
    // formula for find Centered
    // Trigunal number nth term
    return (3 * n * n +
            3 * n + 2) / 2;
}
 
// Driver Code
static public void Main ()
{
 
// For 3rd Centered
// Trigunal number
int n = 3;
Console.WriteLine(Centered_Trigunal_num(n));
 
// For 12th Centered
// Trigunal number
n = 12;
Console.WriteLine(Centered_Trigunal_num(n));
}
}
 
// This code is contributed by akt_mit

Javascript

// javascript Program to find
// the nth Centered
// Triangular number
 
    // function for Centered
    // Trigunal number
    function Centered_Trigunal_num(n)
    {
     
        // formula for find Centered
        // Trigunal number nth term
        return (3 * n * n + 3 * n + 2) / 2;
    }
 
    // Driver Code
     
        // For 3rd Centered
        // Trigunal number
        var n = 3;
        document.write(Centered_Trigunal_num(n)+"<br/>");
 
        // For 12th Centered
        // Trigunal number
        n = 12;
        document.write(Centered_Trigunal_num(n)+"<br/>");
 
// This code is contributed by Rajput-Ji

输出 ：

19
235