# Padovan Sequence

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.

**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) */` `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.*/` |

## Python3

`# 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.*/` |

## PHP

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

## Javascript

`<script>` `// 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.` `</script>` |

Output:

21

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