Padovan Sequence similar to Fibonacci sequence with similar recursive structure. The recursive formula is,

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

Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55……
Spiral of squares with side lengths which follow the Fibonacci sequence.

Image Source : https://en.wikipedia.org/wiki/Fibonacci_number

Padovan Sequence: 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37,…..
Spiral of equilateral triangles with side lengths which follow the Padovan sequence.

Examples:

```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<iostream>
using namespace std;

/* Function to calculate padovan number P(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;
return 0;
}
```

## Python

```# Python program to find n'th term in Padovan
# Sequence using Dynamic Programming

# Function to calculate padovan number P(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
```

Output:

```21
```

# GATE CS Corner    Company Wise Coding Practice

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