# Python Program for Fibonacci numbers

The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

F_{n}= F_{n-1}+ F_{n-2}

with seed values

F_{0}= 0 and F_{1}= 1.

**Method 1 ( Use recursion ) :**

## Python3

`# Function for nth Fibonacci number` `def` `Fibonacci(n):` ` ` ` ` `# Check if input is 0 then it will` ` ` `# print incorrect input` ` ` `if` `n < ` `0` `:` ` ` `print` `(` `"Incorrect input"` `)` ` ` `# Check if n is 0` ` ` `# then it will return 0` ` ` `elif` `n ` `=` `=` `0` `:` ` ` `return` `0` ` ` `# Check if n is 1,2` ` ` `# it will return 1` ` ` `elif` `n ` `=` `=` `1` `or` `n ` `=` `=` `2` `:` ` ` `return` `1` ` ` `else` `:` ` ` `return` `Fibonacci(n` `-` `1` `) ` `+` `Fibonacci(n` `-` `2` `)` `# Driver Program` `print` `(Fibonacci(` `9` `))` `# This code is contributed by Saket Modi` `# then corrected and improved by Himanshu Kanojiya` |

**Output**

34

**Method 2 ( Use Dynamic Programming ) :**

## Python3

`# Function for nth fibonacci` `# number - Dynamic Programming` `# Taking 1st two fibonacci numbers as 0 and 1` `FibArray ` `=` `[` `0` `, ` `1` `]` `def` `fibonacci(n):` ` ` ` ` `# Check is n is less` ` ` `# than 0` ` ` `if` `n <` `=` `0` `:` ` ` `print` `(` `"Incorrect input"` `)` ` ` ` ` `# Check is n is less` ` ` `# than len(FibArray)` ` ` `elif` `n <` `=` `len` `(FibArray):` ` ` `return` `FibArray[n ` `-` `1` `]` ` ` `else` `:` ` ` `temp_fib ` `=` `fibonacci(n ` `-` `1` `) ` `+` `fibonacci(n ` `-` `2` `)` ` ` `FibArray.append(temp_fib)` ` ` `return` `temp_fib` `# Driver Program` `print` `(fibonacci(` `9` `))` `# This code is contributed by Saket Modi` |

**Output**

21

**Method 3 ( Space Optimized):**

## Python

`# Function for nth fibonacci` `# number - Space Optimisation` `# Taking 1st two fibonacci numbers as 0 and 1` `def` `fibonacci(n):` ` ` `a ` `=` `0` ` ` `b ` `=` `1` ` ` ` ` `# Check is n is less` ` ` `# than 0` ` ` `if` `n < ` `0` `:` ` ` `print` `(` `"Incorrect input"` `)` ` ` ` ` `# Check is n is equal` ` ` `# to 0` ` ` `elif` `n ` `=` `=` `0` `:` ` ` `return` `0` ` ` ` ` `# Check if n is equal to 1` ` ` `elif` `n ` `=` `=` `1` `:` ` ` `return` `b` ` ` `else` `:` ` ` `for` `i ` `in` `range` `(` `1` `, n):` ` ` `c ` `=` `a ` `+` `b` ` ` `a ` `=` `b` ` ` `b ` `=` `c` ` ` `return` `b` `# Driver Program` `print` `(fibonacci(` `9` `))` `# This code is contributed by Saket Modi` `# Then corrected and improved by Himanshu Kanojiya` |

**Output**

34

Please refer complete article on Program for Fibonacci numbers for more details!