NTribonacci number problem bottom up approach dynamic programming

NTribonacci number Dynamic Programming Problem

The Tribonacci sequence Tn is defined as follows: T0 = 0, T1 = 1, T2 = 1, and Tn+3 = Tn + Tn+1 + Tn+2 for n >= 0. Given n, return the value of Tn.

1. Why this is a dp problem - because we are asked to generate fibonacci number whcih depends on the last number fibonacci, so its a repeated sub problem
2. During recursion we would be able to calculate previous number fibonacci.
3. The code snippet shows reverse recurssion, starting from n-1 things are calculated till we reach the starting
4. The code below shows bottom up memoization with recursion

    System.out.println(tribonacciNumber.nTribonacciNumber(n, dp))

   private int nTribonacciNumberBottomUp(int n, int dp[]){
      /**This is a top down apprach with memoziation */
        if(n < 3) {
          return n == 0 ? 0 : 1;
        }
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 1;
        for (int i=3; i <= n ; i++) {
           dp[i] = dp[i-1] + dp[i-2] + dp[i-3];
        }
        return dp[n];
    }