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Python | sympy.fibonacci() method

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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 nth Fibonacci number.

Example #1: 

Python3

# 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 nth Fibonacci polynomial. k – It denotes the variable in the Fibonacci polynomial. Returns: Returns  the nth Fibonacci polynomial in k, Fn(k)

Example #2: 

Python3

# 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: 

Python3

# 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


Last Updated : 15 Nov, 2022
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