PYTHON

Fibonacci numbers

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

Fibonacci number

def fibonacciVal(n):  if n == 0:    return 0  elif n == 1:    return 1  else:    return fibonacciVal(n-1) + fibonacciVal(n-2)

fibonacci numbers

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

fibonacci numbers

0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368
75025
121393
196418
317811
514229
832040
1346269
2178309
3524578
5702887
9227465
14930352
24157817
39088169
63245986

Fibonacci numbers

function Fibonacci(num){
	        var before = 0;
	        var actual = 1;
	        var next = 1;

	        for(let i = 0; i < num; i++){
		        console.log(next)
		        before = actual + next;
		        actual = next
		        next = before
	        }
        }

        Fibonacci(100);

Fibonacci numbers

python fibo.py <arguments>

fibonacci numbers

f(n) = f(n-1) + f(n-2) 
                                  f(6)
                                   ^
  			                       /
                f(5)               +                       f(4)
                ^
               /                                           /
                
        f(4)    +           f(3)                     f(3)    +    f(2)
       ^                       ^                     ^              ^
      /                       /                    /            /
   
 f(3)   +       f(2)            f(2) +f(1)       f(2) + f(1)   f(1) +  f(0)             
   ^              ^                ^                ^
   /             /                /              /
    
f(2) + f(1)      f(1) +  f(0)     f(1)+ f(0)       f(1) + f(0)         
  ^
  /
f(1) +  f(0) 
  
//f(6) = 8   ==>  f(1)*8    f(1) appears 8 times 
 double feb  = (1/Math.pow(5,0.5)) * (Math.pow((1+Math.pow(5,0.5))/2,n)) - (1/Math.pow(5,0.5))* (Math.pow((1-Math.pow(5,0.5))/2,n));  
  
f(1) == 1;