# 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()