n steps with 1, 2 or 3 steps taken. How many ways to get to the top?

Question

If we have n steps and we can go up 1 or 2 steps at a time, there is a Fibonacci relation between the number of steps and the ways to climb them. IF and ONLY if we do not co

Answer 1

Java recursive implementation based on Michał's answer:

public class Tribonacci {
    // k(0) = 1
    // k(1) = 1
    // k(2) = 2
    // k(3) = 4
    // ...
    // k(n) = k(n-3) + k(n-2) + k(n - 1)

    static int get(int n) {
        if (n == 0) {
            return 1;
        } if (n == 1) {
            return 1;
        } else if (n == 2) {
            return 2;
        //} else if (n == 3) {
        //    return 4;
        } else {
            return get(n - 3) + get(n - 2) + get(n - 1);
        }
    }

    public static void main(String[] args) {
        System.out.println("Tribonacci sequence");
        System.out.println(Tribonacci.get(1));
        System.out.println(Tribonacci.get(2));
        System.out.println(Tribonacci.get(3));
        System.out.println(Tribonacci.get(4));
        System.out.println(Tribonacci.get(5));
        System.out.println(Tribonacci.get(6));
    }
}