feat: add Pell number algorithm

Maths/PellNumber.js

@@ -0,0 +1,28 @@
+/**
+ * @function pellNumber
+ * @description Pell numbers are an infinite sequence of integers similar
+ *   to Fibonacci. Each number is the sum of twice the previous number
+ *   and the number before that.
+ *   Sequence: 0, 1, 2, 5, 12, 29, 70, 169...
+ * @param {number} n - The position in the Pell sequence (0-indexed)
+ * @returns {number} - The nth Pell number
+ * @see https://en.wikipedia.org/wiki/Pell_number
+ * @example pellNumber(0) => 0
+ * @example pellNumber(1) => 1
+ * @example pellNumber(4) => 12
+ */
+const pellNumber = (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, 2 * b + a]
+  }
+  return b
+}
+
+export { pellNumber }

Maths/test/PellNumber.test.js

@@ -0,0 +1,47 @@
+import { pellNumber } from '../PellNumber.js'
+
+describe('pellNumber', () => {
+  test('pellNumber(0) returns 0', () => {
+    expect(pellNumber(0)).toBe(0)
+  })
+
+  test('pellNumber(1) returns 1', () => {
+    expect(pellNumber(1)).toBe(1)
+  })
+
+  test('pellNumber(2) returns 2', () => {
+    expect(pellNumber(2)).toBe(2)
+  })
+
+  test('pellNumber(3) returns 5', () => {
+    expect(pellNumber(3)).toBe(5)
+  })
+
+  test('pellNumber(4) returns 12', () => {
+    expect(pellNumber(4)).toBe(12)
+  })
+
+  test('pellNumber(5) returns 29', () => {
+    expect(pellNumber(5)).toBe(29)
+  })
+
+  test('pellNumber(6) returns 70', () => {
+    expect(pellNumber(6)).toBe(70)
+  })
+
+  test('pellNumber(7) returns 169', () => {
+    expect(pellNumber(7)).toBe(169)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => pellNumber(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => pellNumber(1.5)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for string input', () => {
+    expect(() => pellNumber('4')).toThrow(TypeError)
+  })
+})