Python| sympy.tribonacci() 方法

借助sympy.tribonacci()方法，我们可以在 SymPy 中找到 Tribonacci 数和 Tribonacci 多项式。

tribonacci(n) -

Tribonacci 数是由初始项定义的整数序列$T_0 = 0$ , $T_1 = 1$ , $T_2 = 1$和三项递推关系$T_n = T_{n-1} + T_{n-2} + T_{n-3}$ .

Syntax: tribonacci(n)

Parameter:
n – It denotes the number upto which Tribonacci number is to be calculated.

Returns: Returns the n^th Tribonacci number.

示例 #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))  

输出：

Value of n = 7
Value of nth tribonacci number : 24

tribonacci(n, k) -

Tribonacci 多项式定义为$T_0(k) = 0$ , $T_1(k) = 1$ , $T_2(k) = k^2$和$T_n(k) = k^2 T_{n-1}(k) + k T_{n-2}(k) + T_{n-3}(k)$为了$n > 2$ .对于所有正整数$n$ , $T_n(1) = T_n$ .

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)

示例 #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))  

输出：

Value of n = 5 and k = x
The nth tribonacci polynomial : x**8 + 3*x**5 + 3*x**2

示例#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))  

输出：

Value of n = 6 and k = 3
The nth tribonacci polynomial value : 68289