NTribonacci number problem top down 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 top down memoization with recursion

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

    private int nTribonacciNumber(int n, int dp[]){
      /**This is a top down apprach with memoziation */
        if(n < 0) {
          return 0;
        }
        if( n == 0) {
          return 0;
        }
        if(n == 1 || n ==2 ){
          return 1;
        }
        if(dp[n] >=0) { //way of using the saved values
          System.out.println("Reusing results : "+ dp[n]);
          return dp[n];
        }
        dp[n] = nTribonacciNumber(n-2, dp) + nTribonacciNumber(n-1, dp) + nTribonacciNumber(n-3, dp);
        return dp[n];
    }