> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/sidef-lang/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/sidef-lang/programming_tasks/f/fibonacci_sequence.md).

# Fibonacci sequence

### Iterative

```ruby
func fib_iter(n) {
    var (a, b) = (0, 1)
    { (a, b) = (b, a+b) } * n
    return a
}
```

### Recursive

```ruby
func fib_rec(n) {
    n < 2 ? n : (__FUNC__(n-1) + __FUNC__(n-2))
}
```

### Recursive with memoization

```ruby
func fib_mem (n) is cached {
    n < 2 ? n : (__FUNC__(n-1) + __FUNC__(n-2))
}
```

### Closed-form

```ruby
func fib_closed(n) {
    define S = (1.25.sqrt + 0.5)
    define T = (-S + 1)
    (S**n - T**n) / (-T + S) -> round
}
```

### Built-in

```ruby
say fib(12)        #=> 144
```