帕多万序列

Padovan序列类似于Fibonacci序列，具有类似的递归结构。递归公式为

P(n) = P(n-2) + P(n-3)
  P(0) = P(1) = P(2) = 1 

斐波那契数列： 0、1、1、2、3、5、8、13、21、34、55……
正方形螺旋的边长遵循斐波那契数列。

Padovan序列：1、1、1、2、2、3、4、5、7、9、12、16、21、28、37 ，…..
等边三角形的螺旋形状，其边长遵循Padovan序列。

例子：

For Padovan Sequence:
P0 = P1 = P2 = 1 ,
P(7) = P(5) + P(4)
     = P(3) + P(2) + P(2) + P(1)
     = P(2) + P(1) + 1 + 1 + 1
     = 1 + 1 + 1 + 1 + 1 
     = 5

C++

// C++ program to find n'th term in Padovan Sequence
// using Dynamic Programming
#include
using namespace std;
 
/* Function to calculate padovan number P(n) */
int pad(int n)
{
    /* 0th ,1st and 2nd number of the series are 1*/
    int pPrevPrev = 1, pPrev = 1, pCurr = 1, pNext = 1;
 
    for (int i=3; i<=n; i++)
    {
        pNext = pPrevPrev + pPrev;
        pPrevPrev = pPrev;
        pPrev = pCurr;
        pCurr = pNext;
    }
 
    return pNext;
}
 
/* Driver Program */
int main()
{
    int n = 12;
    cout << pad(n);
    return 0;
}

Java

// Java program to find n'th term
// in Padovan Sequence using
// Dynamic Programming
import java.io.*;
 
class GFG {
     
    /* Function to calculate
    padovan number P(n) */
    static int pad(int n)
    {
       int []padv=new int[n]; //create array to store padovan values
       padv[0]=padv[1]=padv[2]=1;
        for (int i = 3; i <= n; i++) {
         padv[i]=padv[i-2]+padv[i-3];  
        }
        return padv[n-1];
 
         
    }
 
    /* Driver Program */
    public static void main(String args[])
    {
        int n = 12;
        System.out.println(pad(n));
    }
}
 
/*This code is contributed by Kanjam Bhat Lidhoo.*/

Python

# Python program to find n'th term in Padovan
# Sequence using Dynamic Programming
 
# Function to calculate padovan number P(n)
def pad(n):
 
    # 0th ,1st and 2nd number of the series are 1
    pPrevPrev, pPrev, pCurr, pNext = 1, 1, 1, 1
 
    # Find n'th Padovan number using recursive
    # formula.
    for i in range(3, n+1):
        pNext = pPrevPrev + pPrev
        pPrevPrev = pPrev
        pPrev = pCurr
        pCurr = pNext
 
    return pNext;
 
# Driver Code
print pad(12)

C#

// C# program to find n'th term
// in Padovan Sequence using
// Dynamic Programming
using System;
 
class GFG {
 
    /* Function to calculate
    padovan number P(n) */
    static int pad(int n)
    {
         
        /* 0th, 1st and 2nd number
        of the series are 1*/
        int pPrevPrev = 1, pPrev = 1,
            pCurr = 1, pNext = 1;
 
        for (int i = 3; i <= n; i++) {
            pNext = pPrevPrev + pPrev;
            pPrevPrev = pPrev;
            pPrev = pCurr;
            pCurr = pNext;
        }
 
        return pNext;
    }
 
    /* Driver Program */
    public static void Main()
    {
        int n = 12;
         
        Console.WriteLine(pad(n));
    }
}
 
/*This code is contributed by vt_m.*/

Javascript

// Javascript program to find n'th
// term in Padovan Sequence
// using Dynamic Programming
 
// Function to calculate
// padovan number P(n)
function pad(n) {
 
    // 0th ,1st and 2nd number
    // of the series are 1
    let pPrevPrev = 1;
    let pPrev = 1;
    let pCurr = 1;
    let pNext = 1;
 
    for (let i = 3; i <= n; i++) {
        pNext = pPrevPrev + pPrev;
        pPrevPrev = pPrev;
        pPrev = pCurr;
        pCurr = pNext;
    }
 
    return pNext;
}
 
// Driver Code
let n = 12;
document.write(pad(n));
 
// This code is contributed by gfgking.

输出：

21