-The Lucas numbers are a sequence of integers, named after Édouard Lucas, which are closely related to the Fibonacci sequence. In fact, they are defined in very much the same way: Ln if n = 0; if n = 1; if n>1 2 1 Ln-1+ Ln-2 -Using the recursive description above, write a private static int method in Week4Main called lucask which takes one parameter, n, and computes the n'h Lucas number Ln.
1. Import the necessary Java libraries (java.util.*) for input.
2. Define a class called `Week4Main`.
3. In the `main` method:
a. Create a `Scanner` object (`sc`) to read user input from the console.
b. Prompt the user to enter an integer `n` which represents the index of the Lucas number they want to calculate.
c. Read the integer `n` from the user.
d. Call the `lucasR` method with the value of `n` and store the result in the `result` variable.
e. Print the calculated Lucas number along with a message.
4. In the `lucasR` method:
a. Check if `n` is equal to 0. If so, return 2, as the 0th Lucas number is defined as 2.
b. Check if `n` is equal to 1. If so, return 1, as the 1st Lucas number is defined as 1.
c. For values of `n` greater than 1, use recursion:
i. Call `lucasR(n - 1)` to calculate the (n-1)th Lucas number.
ii. Call `lucasR(n - 2)` to calculate the (n-2)nd Lucas number.
iii. Add the results of the two recursive calls and return the sum, which represents the nth Lucas number.
The program keeps calling the `lucasR` method recursively until it reaches one of the base cases (n = 0 or n = 1), and then it computes and returns the nth Lucas number based on the recursive definition.
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