With the help of sympy.tribonacci() method, we can find Tribonacci number and Tribonacci polynomial in SymPy.
tribonacci(n) –
The Tribonacci numbers are the integer sequence defined by the initial terms 
, , and the three-term recurrence relation .
Syntax: tribonacci(n)
Parameter:
n – It denotes the number upto which Tribonacci number is to be calculated.Returns: Returns the nth Tribonacci number.
Example #1:
# import sympy from sympy import * n = 7print("Value of n = {}".format(n)) # Use sympy.tribonacci() method nth_tribonacci = tribonacci(n) print("Value of nth tribonacci number : {}".format(nth_tribonacci)) |
Output:
Value of n = 7 Value of nth tribonacci number : 24
tribonacci(n, k) –
The Tribonacci polynomials are defined by , , and for . For all positive integers , .
Syntax: tribonacci(n, k)
Parameter:
n – It denotes the nth Tribonacci polynomial.
k – It denotes the variable in the Tribonacci polynomial.Returns: Returns the nth Tribonacci polynomial in k, Tn(k)
Example #2:
# import sympy from sympy import * n = 5k = symbols('x') print("Value of n = {} and k = {}".format(n, k)) # Use sympy.tribonacci() method nth_tribonacci_poly = tribonacci(n, k) print("The nth tribonacci polynomial : {}".format(nth_tribonacci_poly)) |
Output:
Value of n = 5 and k = x The nth tribonacci polynomial : x**8 + 3*x**5 + 3*x**2
Example #3:
# import sympy from sympy import * n = 6k = 3print("Value of n = {} and k = {}".format(n, k)) # Use sympy.tribonacci() method nth_tribonacci_poly = tribonacci(n, k) print("The nth tribonacci polynomial value : {}".format(nth_tribonacci_poly)) |
Output:
Value of n = 6 and k = 3 The nth tribonacci polynomial value : 68289
