Python | sympy.fibonacci() method

With the help of sympy.fibonacci() method, we can find the Fibonacci number and Fibonacci polynomial in SymPy. 

fibonacci(n) - The Fibonacci numbers are the integer sequence defined by the initial terms F_0 = 0 , F_1 = 1 and the two-term recurrence relation F_n = F_{n-1} + F_{n-2} .

Syntax: fibonacci(n) Parameter: n - It denotes the number upto which Fibonacci number is to be calculated. Returns: Returns the n^th Fibonacci number.

Example #1: 

# import sympy 
from sympy import * 
n = 7
print("Value of n = {}".format(n))
 
# Use sympy.fibonacci() method 
nth_fibonacci = fibonacci(n)  
    
print("Value of nth fibonacci number : {}".format(nth_fibonacci))  

Output:

Value of n = 7
Value of nth fibonacci number : 13

fibonacci(n, k) -

The Fibonacci polynomials are defined by F_1(k) = 1 , F_2(k) = k , and F_n(k) = k*F_{n-1}(k) + F_{n-2}(k) for n > 2 . For all positive integers n , F_n(1) = F_n .

Syntax: fibonacci(n, k) Parameter: n - It denotes the n^th Fibonacci polynomial. k - It denotes the variable in the Fibonacci polynomial. Returns: Returns  the nth Fibonacci polynomial in k, F_n(k)

Example #2: 

# import sympy 
from sympy import * 
n = 5
k = symbols('x')
print("Value of n = {} and k = {}".format(n, k))
 
# Use sympy.fibonacci() method 
nth_fibonacci_poly = fibonacci(n, k)  
    
print("The nth fibonacci polynomial : {}".format(nth_fibonacci_poly))  

Output:

Value of n = 5 and k = x
The nth fibonacci polynomial : x**4 + 3*x**2 + 1

Example #3: 

# import sympy 
from sympy import * 
n = 6
k = 3
print("Value of n = {} and k = {}".format(n, k))
 
# Use sympy.fibonacci() method 
nth_fibonacci_poly = fibonacci(n, k)  
    
print("The nth fibonacci polynomial value : {}".format(nth_fibonacci_poly))  

Output:

Value of n = 6 and k = 3
The nth fibonacci polynomial value : 360