Python | sympy.tribonacci() method

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 n^th Tribonacci number.

Example #1:

# import sympy
from sympy import *

n = 7
print("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 n^th Tribonacci polynomial. k – It denotes the variable in the Tribonacci polynomial. Returns: Returns the nth Tribonacci polynomial in k, T_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.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 = 6
k = 3
print("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