Add Tribonacci Numbers (fixes #4646) (#4959)

src/main/java/com/thealgorithms/dynamicprogramming/Tribonacci.java

@@ -0,0 +1,30 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * The {@code Tribonacci} class provides a method to compute the n-th number in the Tribonacci sequence.
+ * N-th Tribonacci Number - https://leetcode.com/problems/n-th-tribonacci-number/description/
+ */
+public class Tribonacci {
+
+    /**
+     * Computes the n-th Tribonacci number.
+     *
+     * @param n the index of the Tribonacci number to compute
+     * @return the n-th Tribonacci number
+     */
+    public static int compute(int n) {
+        if (n == 0) return 0;
+        if (n == 1 || n == 2) return 1;
+
+        int first = 0, second = 1, third = 1;
+
+        for (int i = 3; i <= n; i++) {
+            int next = first + second + third;
+            first = second;
+            second = third;
+            third = next;
+        }
+
+        return third;
+    }
+}