feat: add Padovan sequence algorithm

Maths/PadovanSequence.js

@@ -0,0 +1,27 @@
+/**
+ * @function padovanSequence
+ * @description The Padovan sequence is similar to Fibonacci but each
+ *   number is the sum of the second and third preceding numbers.
+ *   Sequence: 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16...
+ * @param {number} n - The position in the Padovan sequence (0-indexed)
+ * @returns {number} - The nth Padovan number
+ * @see https://en.wikipedia.org/wiki/Padovan_sequence
+ * @example padovanSequence(0) => 1
+ * @example padovanSequence(5) => 3
+ * @example padovanSequence(7) => 5
+ */
+const padovanSequence = (n) => {
+  if (!Number.isInteger(n) || n < 0) {
+    throw new TypeError('Input must be a non-negative integer')
+  }
+  if (n === 0 || n === 1 || n === 2) return 1
+  let a = 1
+  let b = 1
+  let c = 1
+  for (let i = 3; i <= n; i++) {
+    ;[a, b, c] = [b, c, a + b]
+  }
+  return c
+}
+
+export { padovanSequence }

Maths/test/PadovanSequence.test.js

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