CodeWars - Kata - Tribonacci Sequence

problem.md

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 (except in C return NULL) 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 :)]

solution.spec.ts

import { assert } from "chai";
import { tribonacci } from "./solution";

const tester = (sig: [number, number, number], n: number, exp: number[]) => it(`tribonacci([${sig[0]}, ${sig[1]}, ${sig[2]}], ${n})`, () => assert.deepStrictEqual(tribonacci(sig, n), exp));
describe("basic tests", () => {
  tester([1, 1, 1], 10, [1, 1, 1, 3, 5, 9, 17, 31, 57, 105]);
  tester([0, 0, 1], 10, [0, 0, 1, 1, 2, 4, 7, 13, 24, 44]);
  tester([0, 1, 1], 10, [0, 1, 1, 2, 4, 7, 13, 24, 44, 81]);
  tester([1, 0, 0], 10, [1, 0, 0, 1, 1, 2, 4, 7, 13, 24]);
  tester([0, 0, 0], 10, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
  tester([1, 2, 3], 10, [1, 2, 3, 6, 11, 20, 37, 68, 125, 230]);
  tester([3, 2, 1], 10, [3, 2, 1, 6, 9, 16, 31, 56, 103, 190]);
  tester([1, 1, 1], 1, [1]);
  tester([300, 200, 100], 0, []);
  tester([0.5, 0.5, 0.5], 30, [0.5, 0.5, 0.5, 1.5, 2.5, 4.5, 8.5, 15.5, 28.5, 52.5, 96.5, 177.5, 326.5, 600.5, 1104.5, 2031.5, 3736.5, 6872.5, 12640.5, 23249.5, 42762.5, 78652.5, 144664.5, 266079.5, 489396.5, 900140.5, 1655616.5, 3045153.5, 5600910.5, 10301680.5]);
});

solution.ts

export function tribonacci(signature: [number, number, number], n: number): number[] {
    let trib = signature;
    for (let i = 3; i < n; i++) {
      trib.push((trib[i-1] + trib[i-2] + trib[i-3]));
    }
    return trib.slice(0, n);
}

https://www.codewars.com/kata/556deca17c58da83c00002db/train/typescript