feat: add Motzkin number algorithm

Maths/MotzkinNumber.js

@@ -0,0 +1,29 @@
+/**
+ * @function motzkinNumber
+ * @description Motzkin numbers count the number of different ways of
+ *   drawing non-intersecting chords between points on a circle.
+ *   Sequence: 1, 1, 2, 4, 9, 21, 51, 127, 323, 835...
+ * @param {number} n - The position in the Motzkin sequence (0-indexed)
+ * @returns {number} - The nth Motzkin number
+ * @see https://en.wikipedia.org/wiki/Motzkin_number
+ * @example motzkinNumber(0) => 1
+ * @example motzkinNumber(4) => 9
+ * @example motzkinNumber(6) => 51
+ */
+const motzkinNumber = (n) => {
+  if (!Number.isInteger(n) || n < 0) {
+    throw new TypeError('Input must be a non-negative integer')
+  }
+  if (n === 0 || n === 1) return 1
+  const dp = new Array(n + 1).fill(0)
+  dp[0] = 1
+  dp[1] = 1
+  for (let i = 2; i <= n; i++) {
+    dp[i] = Math.floor(
+      ((2 * i + 1) * dp[i - 1] + (3 * i - 3) * dp[i - 2]) / (i + 2)
+    )
+  }
+  return dp[n]
+}
+
+export { motzkinNumber }

Maths/test/MotzkinNumber.test.js

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+import { motzkinNumber } from '../MotzkinNumber.js'
+
+describe('motzkinNumber', () => {
+  test('motzkinNumber(0) returns 1', () => {
+    expect(motzkinNumber(0)).toBe(1)
+  })
+
+  test('motzkinNumber(1) returns 1', () => {
+    expect(motzkinNumber(1)).toBe(1)
+  })
+
+  test('motzkinNumber(2) returns 2', () => {
+    expect(motzkinNumber(2)).toBe(2)
+  })
+
+  test('motzkinNumber(3) returns 4', () => {
+    expect(motzkinNumber(3)).toBe(4)
+  })
+
+  test('motzkinNumber(4) returns 9', () => {
+    expect(motzkinNumber(4)).toBe(9)
+  })
+
+  test('motzkinNumber(5) returns 21', () => {
+    expect(motzkinNumber(5)).toBe(21)
+  })
+
+  test('motzkinNumber(6) returns 51', () => {
+    expect(motzkinNumber(6)).toBe(51)
+  })
+
+  test('motzkinNumber(7) returns 127', () => {
+    expect(motzkinNumber(7)).toBe(127)
+  })
+
+  test('motzkinNumber(8) returns 323', () => {
+    expect(motzkinNumber(8)).toBe(323)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => motzkinNumber(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => motzkinNumber(1.5)).toThrow(TypeError)
+  })
+})