Python: Fibonacci numbers

Fibonacci number

Fibonacci sequence is a very mysterious sequence of numbers which can be described by equation:

• F₀ = 0, F₁ = 1,
• F_n = F_n-1 + F_n-2

In this example, we will make a function, calculating Fibonacci number

def fibonacci(n):
    fib1, fib2 = 0, 1
    for i in range (2, n + 1):
        fib1, fib2 = fib2, fib1 + fib2
    return fib2;

Fibonacci sequence

We can print out Fibonacci sequence in cycle

n = 10

fib1, fib2 = 0, 1
print(fib1, fib2, end=' ') # 0 1 
for i in range(2, n+1):
    fib1, fib2 = fib2, fib1 + fib2
    print(fib2, end=' ') # 1 2 3 5 8 13 21 34 55

Bine equation for Fibonacci number

It is possible to use Bine equation for calculations:

• F_n = [φⁿ / √5 ] - []-mean rounding
• φ = (1 + √5)/2

def fibonacci(n):
    return pow(2 << n, n + 1, (4 << 2 * n) - (2 << n) - 1) % (2 << n)

print(fibonacci(71)) # 308061521170129

Published: 2021-11-06 22:56:55
Updated: 2021-11-06 23:24:05

Last 10 artitles

• 2023-12-25 01:48:38 - In-place and out-place Numpy functions
• 2023-12-25 00:58:08 - First order ordinary differential equations
• 2023-12-25 00:22:15 - How to increase swap space in Ubuntu
• 2023-12-24 04:03:12 - How to accelerate math calculations with Numba and Cython
• 2023-12-19 00:38:20 - 3 ways of function caching in Python
• 2023-12-19 00:16:55 - Accelerating Python
• 2023-12-16 12:26:55 - BioPython
• 2023-12-02 11:05:34 - Reading FITS files with astropy
• 2023-12-02 05:23:42 - Astropy
• 2023-12-01 00:33:16 - Circle length calculation with the Monte-Carlo method

9 popular artitles

• Python Panda (3427)
• Python NumPy (2975)
• Python DICTionary HowTo (1591)
• Python LIST HowTo (1468)
• Python (1421)
• Python Generators (1279)
• Python: How to make absolute links in BeautifulSoup (1076)
• Programming language (967)
• NumPy: What the difference between mgrid and meshgrid (939)