Tribonacci Sequence

src/algorithms/math/tribonacci/README.md

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+# Tribonacci Number
+
+The tribonacci numbers are a homogeneous linear recurrence with constant coefficients of order 3 with signature (0, 0, 1), inspired from the Fibonacci numbers (which are of order 2 with signature (0, 1)), i.e.
+
+`0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136 ...`
+
+## References
+
+- [Brilliant](https://brilliant.org/wiki/tribonacci-sequence/)
+- [Oeis](http://oeis.org/wiki/Tribonacci_numbers)

src/algorithms/math/tribonacci/__test__/tribonacci.test.js

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+import tribonacci from '../tribonacci';
+
+describe('tribonacci', () => {
+  it('should calculate tribonacci correctly', () => {
+    expect(tribonacci(1)).toEqual([0]);
+    expect(tribonacci(2)).toEqual([0, 0]);
+    expect(tribonacci(3)).toEqual([0, 0, 1]);
+    expect(tribonacci(4)).toEqual([0, 0, 1, 1]);
+    expect(tribonacci(5)).toEqual([0, 0, 1, 1, 2]);
+    expect(tribonacci(6)).toEqual([0, 0, 1, 1, 2, 4]);
+    expect(tribonacci(7)).toEqual([0, 0, 1, 1, 2, 4, 7]);
+    expect(tribonacci(8)).toEqual([0, 0, 1, 1, 2, 4, 7, 13]);
+    expect(tribonacci(9)).toEqual([0, 0, 1, 1, 2, 4, 7, 13, 24]);
+    expect(tribonacci(10)).toEqual([0, 0, 1, 1, 2, 4, 7, 13, 24, 44]);
+  });
+});

src/algorithms/math/tribonacci/__test__/tribonacciNth.test.js

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+import tribonacciNth from '../tribonacciNth';
+
+describe('tribonacciNth', () => {
+  it('should calculate tribonacci correctly', () => {
+    expect(tribonacciNth(1)).toBe(0);
+    expect(tribonacciNth(2)).toBe(1);
+    expect(tribonacciNth(3)).toBe(1);
+    expect(tribonacciNth(4)).toBe(2);
+    expect(tribonacciNth(5)).toBe(4);
+    expect(tribonacciNth(6)).toBe(7);
+    expect(tribonacciNth(7)).toBe(13);
+    expect(tribonacciNth(8)).toBe(24);
+    expect(tribonacciNth(20)).toBe(35890);
+    expect(tribonacciNth(30)).toBe(15902591);
+    expect(tribonacciNth(50)).toBe(3122171529233);
+  });
+});

src/algorithms/math/tribonacci/tribonacci.js

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+/**
+ * Return a tribonacci sequence as an array.
+ *
+ * @param n
+ * @return {number[]}
+ */
+export default function tribonacci(n) {
+  const tribSequence = [0];
+
+  if (n >= 2) {
+    tribSequence.push(0);
+  }
+
+  let currentValue = 1;
+
+  for (let i = 2; i < n; i += 1) {
+    tribSequence.push(currentValue);
+    currentValue += tribSequence[i - 1] + tribSequence[i - 2];
+  }
+
+  return tribSequence;
+}

src/algorithms/math/tribonacci/tribonacciNth.js

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+/**
+ * Calculate tribonacci number at specific position using Dynamic Programming approach.
+ *
+ * @param n
+ * @return {number}
+ */
+export default function tribonacciNth(n) {
+  const tribSequence = [0, 0, 1];
+  let currentValue = 1;
+
+  for (let i = 3; i <= n; i += 1) {
+    tribSequence.push(currentValue);
+    currentValue += tribSequence[i - 1] + tribSequence[i - 2];
+  }
+
+  return tribSequence[n];
+}