feat: add Jacobsthal number algorithm

Maths/JacobsthalNumber.js

@@ -0,0 +1,27 @@
+/**
+ * @function jacobsthalNumber
+ * @description Jacobsthal numbers are a sequence where each number is
+ *   the sum of the previous number and twice the number before that.
+ *   Sequence: 0, 1, 1, 3, 5, 11, 21, 43, 85, 171...
+ * @param {number} n - The position in the Jacobsthal sequence (0-indexed)
+ * @returns {number} - The nth Jacobsthal number
+ * @see https://en.wikipedia.org/wiki/Jacobsthal_number
+ * @example jacobsthalNumber(0) => 0
+ * @example jacobsthalNumber(4) => 5
+ * @example jacobsthalNumber(6) => 21
+ */
+const jacobsthalNumber = (n) => {
+  if (!Number.isInteger(n) || n < 0) {
+    throw new TypeError('Input must be a non-negative integer')
+  }
+  if (n === 0) return 0
+  if (n === 1) return 1
+  let a = 0
+  let b = 1
+  for (let i = 2; i <= n; i++) {
+    ;[a, b] = [b, b + 2 * a]
+  }
+  return b
+}
+
+export { jacobsthalNumber }

Maths/test/JacobsthalNumber.test.js

@@ -0,0 +1,47 @@
+import { jacobsthalNumber } from '../JacobsthalNumber.js'
+
+describe('jacobsthalNumber', () => {
+  test('jacobsthalNumber(0) returns 0', () => {
+    expect(jacobsthalNumber(0)).toBe(0)
+  })
+
+  test('jacobsthalNumber(1) returns 1', () => {
+    expect(jacobsthalNumber(1)).toBe(1)
+  })
+
+  test('jacobsthalNumber(2) returns 1', () => {
+    expect(jacobsthalNumber(2)).toBe(1)
+  })
+
+  test('jacobsthalNumber(3) returns 3', () => {
+    expect(jacobsthalNumber(3)).toBe(3)
+  })
+
+  test('jacobsthalNumber(4) returns 5', () => {
+    expect(jacobsthalNumber(4)).toBe(5)
+  })
+
+  test('jacobsthalNumber(5) returns 11', () => {
+    expect(jacobsthalNumber(5)).toBe(11)
+  })
+
+  test('jacobsthalNumber(6) returns 21', () => {
+    expect(jacobsthalNumber(6)).toBe(21)
+  })
+
+  test('jacobsthalNumber(7) returns 43', () => {
+    expect(jacobsthalNumber(7)).toBe(43)
+  })
+
+  test('jacobsthalNumber(8) returns 85', () => {
+    expect(jacobsthalNumber(8)).toBe(85)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => jacobsthalNumber(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => jacobsthalNumber(1.5)).toThrow(TypeError)
+  })
+})