Python | sympy.fibonacci() method

Last Updated : 14 Jul, 2019

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 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

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fibonacci(n, k) -