feat: Add PadovanSequence Implementation

Author: Rosander0

src/main/java/com/thealgorithms/maths/PadovanSequence.java

@@ -0,0 +1,43 @@
+package com.thealgorithms.maths;
+// author: Vraj Prajapati @Rosander0
+
+/**
+ * The Padovan Sequence is a sequence of integers defined by the recurrence relation:
+ * P(n) = P(n-2) + P(n-3) with initial values P(0) = P(1) = P(2) = 1.
+ * Example: 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37...
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Padovan_sequence">
+ *     Wikipedia: Padovan Sequence</a>
+ */
+public final class PadovanSequence {
+
+    private PadovanSequence() {
+        // Utility class
+    }
+
+    /**
+     * Calculates the nth term of the Padovan Sequence.
+     *
+     * @param n the index of the sequence (must be non-negative)
+     * @return the nth term of the Padovan Sequence
+     */
+    public static long padovan(final int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Input must be non-negative!");
+        }
+        if (n <= 2) {
+            return 1;
+        }
+        long a = 1;
+        long b = 1;
+        long c = 1;
+        long result = 0;
+        for (int i = 3; i <= n; i++) {
+            result = a + b;
+            a = b;
+            b = c;
+            c = result;
+        }
+        return result;
+    }
+}

src/test/java/com/thealgorithms/maths/PadovanSequenceTest.java

@@ -0,0 +1,35 @@
+package com.thealgorithms.maths;
+// author: Vraj Prajapati @Rosander0
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+public class PadovanSequenceTest {
+
+    @Test
+    public void testBaseCase() {
+        assertEquals(1, PadovanSequence.padovan(0));
+        assertEquals(1, PadovanSequence.padovan(1));
+        assertEquals(1, PadovanSequence.padovan(2));
+    }
+
+    @Test
+    public void testKnownValues() {
+        assertEquals(2, PadovanSequence.padovan(3));
+        assertEquals(2, PadovanSequence.padovan(4));
+        assertEquals(3, PadovanSequence.padovan(5));
+        assertEquals(4, PadovanSequence.padovan(6));
+        assertEquals(5, PadovanSequence.padovan(7));
+        assertEquals(7, PadovanSequence.padovan(8));
+        assertEquals(9, PadovanSequence.padovan(9));
+        assertEquals(12, PadovanSequence.padovan(10));
+    }
+
+    @Test
+    public void testInvalidInput() {
+        assertThrows(IllegalArgumentException.class,
+            () -> PadovanSequence.padovan(-1));
+    }
+}