feat: add JacobsthalNumber implementation

Author: Rosander0

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

@@ -0,0 +1,44 @@
+package com.thealgorithms.maths;
+// author: Vraj Prajapati @Rosander0
+
+/**
+ * The Jacobsthal Sequence is a sequence of integers defined by the recurrence relation:
+ * J(n) = J(n-1) + 2*J(n-2) with initial values J(0) = 0, J(1) = 1.
+ * Example: 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341...
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Jacobsthal_number">
+ *     Wikipedia: Jacobsthal Number</a>
+ */
+public final class JacobsthalNumber {
+
+    private JacobsthalNumber() {
+        // Utility class
+    }
+
+    /**
+     * Calculates the nth term of the Jacobsthal Sequence.
+     *
+     * @param n the index of the sequence (must be non-negative)
+     * @return the nth term of the Jacobsthal Sequence
+     */
+    public static long jacobsthal(final int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Input must be non-negative!");
+        }
+        if (n == 0) {
+            return 0;
+        }
+        if (n == 1) {
+            return 1;
+        }
+        long a = 0;
+        long b = 1;
+        long result = 0;
+        for (int i = 2; i <= n; i++) {
+            result = b + 2 * a;
+            a = b;
+            b = result;
+        }
+        return result;
+    }
+}

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

@@ -0,0 +1,34 @@
+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 JacobsthalNumberTest {
+
+    @Test
+    public void testBaseCases() {
+        assertEquals(0, JacobsthalNumber.jacobsthal(0));
+        assertEquals(1, JacobsthalNumber.jacobsthal(1));
+    }
+
+    @Test
+    public void testKnownValues() {
+        assertEquals(1, JacobsthalNumber.jacobsthal(2));
+        assertEquals(3, JacobsthalNumber.jacobsthal(3));
+        assertEquals(5, JacobsthalNumber.jacobsthal(4));
+        assertEquals(11, JacobsthalNumber.jacobsthal(5));
+        assertEquals(21, JacobsthalNumber.jacobsthal(6));
+        assertEquals(43, JacobsthalNumber.jacobsthal(7));
+        assertEquals(85, JacobsthalNumber.jacobsthal(8));
+        assertEquals(171, JacobsthalNumber.jacobsthal(9));
+        assertEquals(341, JacobsthalNumber.jacobsthal(10));
+    }
+
+    @Test
+    public void testInvalidInput() {
+        assertThrows(IllegalArgumentException.class, () -> JacobsthalNumber.jacobsthal(-1));
+    }
+}