Added implementation for Tribonacci sequence using dp (#6356)

* Added implementation for Tribonacci sequence using dp

* Updated parameter name

* Apply suggestions from code review

---------

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

dynamic_programming/tribonacci.py

@@ -0,0 +1,24 @@
+# Tribonacci sequence using Dynamic Programming
+
+
+def tribonacci(num: int) -> list[int]:
+    """
+    Given a number, return first n Tribonacci Numbers.
+    >>> tribonacci(5)
+    [0, 0, 1, 1, 2]
+    >>> tribonacci(8)
+    [0, 0, 1, 1, 2, 4, 7, 13]
+    """
+    dp = [0] * num
+    dp[2] = 1
+
+    for i in range(3, num):
+        dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3]
+
+    return dp
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()