Tribonacci Sequence

Well met with Fibonacci bigger brother, AKA Tribonacci.

As the name may already reveal, it works basically like a Fibonacci, but summing the last 3 (instead of 2) numbers of the sequence to generate the next. And, worse part of it, regrettably I won't get to hear non-native Italian speakers trying to pronounce it :(

So, if we are to start our Tribonacci sequence with [1, 1, 1] as a starting input (AKA signature), we have this sequence:

[1, 1 ,1, 3, 5, 9, 17, 31, ...]

But what if we started with [0, 0, 1] as a signature? As starting with [0, 1] instead of [1, 1] basically shifts the common Fibonacci sequence by once place, you may be tempted to think that we would get the same sequence shifted by 2 places, but that is not the case and we would get:

[0, 0, 1, 1, 2, 4, 7, 13, 24, ...]

Well, you may have guessed it by now, but to be clear: you need to create a fibonacci function that given a signature array/list, returns the first n elements - signature included of the so seeded sequence.

Signature will always contain 3 numbers; n will always be a non-negative number; if n == 0, then return an empty array and be ready for anything else which is not clearly specified ;)

If you enjoyed this kata more advanced and generalized version of it can be found in the Xbonacci kata

[Personal thanks to Professor Jim Fowler on Coursera for his awesome classes that I really recommend to any math enthusiast and for showing me this mathematical curiosity too with his usual contagious passion :)]
Well met with Fibonacci bigger brother, AKA Tribonacci.

As the name may already reveal, it works basically like a Fibonacci, but summing the last 3 (instead of 2) numbers of the sequence to generate the next. And, worse part of it, regrettably I won't get to hear non-native Italian speakers trying to pronounce it :(

So, if we are to start our Tribonacci sequence with [1, 1, 1] as a starting input (AKA signature), we have this sequence:

[1, 1 ,1, 3, 5, 9, 17, 31, ...]

But what if we started with [0, 0, 1] as a signature? As starting with [0, 1] instead of [1, 1] basically shifts the common Fibonacci sequence by once place, you may be tempted to think that we would get the same sequence shifted by 2 places, but that is not the case and we would get:

[0, 0, 1, 1, 2, 4, 7, 13, 24, ...]

Well, you may have guessed it by now, but to be clear: you need to create a fibonacci function that given a signature array/list, returns the first n elements - signature included of the so seeded sequence.

Signature will always contain 3 numbers; n will always be a non-negative number; if n == 0, then return an empty array and be ready for anything else which is not clearly specified ;)

If you enjoyed this kata more advanced and generalized version of it can be found in the Xbonacci kata

[Personal thanks to Professor Jim Fowler on Coursera for his awesome classes that I really recommend to any math enthusiast and for showing me this mathematical curiosity too with his usual contagious passion :)]

Good Solution1:

import java.util.Arrays;

public class Xbonacci {
  public double[] tribonacci(double[] s, int n) {

      double[] tritab=Arrays.copyOf(s, n);
      for(int i=3;i<n;i++){
        tritab[i]=tritab[i-1]+tritab[i-2]+tritab[i-3];
      }
      return tritab;

    }
}

Good Solution2:

public class Xbonacci {

  public double[] tribonacci(double[] s, int n) {
      double[] r = new double[n];
      for(int i = 0; i < n; i++){
        r[i] = (i<3)?s[i]:r[i-3]+r[i-2]+r[i-1];
      }
      return r;
  }
}