Fibonacci Sequence Generator#

Generate Fibonacci sequences and work with Fibonacci numbers, golden ratios, and related mathematical concepts.

Quick Start#

Basic Usage#

The Fibonacci sequence starts with 0, 1, and each subsequent number is the sum of the two preceding ones.

First 10 Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34

Generate First N Numbers#

python

def fibonacci(n):
    """Generate first n Fibonacci numbers."""
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    seq = [0, 1]
    for i in range(2, n):
        seq.append(seq[-1] + seq[-2])
    return seq

Common Operations#

Nth Fibonacci Number (0-indexed)#

python

def nth_fibonacci(n):
    """Get the nth Fibonacci number (0-indexed)."""
    a, b = 0, 1
    for _ in range(n):
        a, b = b, a + b
    return a

Check if Number is Fibonacci#

python

import math

def is_fibonacci(x):
    """Check if x is a Fibonacci number."""
    def is_perfect_square(n):
        s = int(math.sqrt(n))
        return s * s == n
    return is_perfect_square(5 * x * x + 4) or is_perfect_square(5 * x * x - 4)

Golden Ratio Approximation#

As n increases, the ratio F(n+1)/F(n) approaches the golden ratio φ ≈ 1.618033988749895

Related Sequences#

Lucas Numbers#

Similar to Fibonacci but starts with 2, 1

Tribonacci#

Each number is sum of previous three

Fibonacci Sum#

Sum of first n Fibonacci numbers = F(n+2) - 1