Add Trinomial triangle #2651 (#2652)

Maths/TrinomialTriangle.java

@@ -0,0 +1,47 @@
+package Maths;
+
+/**
+ * The trinomial triangle is a variation of Pascal’s triangle. The difference
+ * between the two is that an entry in the trinomial triangle is the sum of the
+ * three (rather than the two in Pasacal’s triangle) entries above it
+ * 
+ * Example Input: n = 4 
+ * Output 
+ * 1 
+ * 1 1 1 
+ * 1 2 3 2 1 
+ * 1 3 6 7 6 3 1
+ */
+public class TrinomialTriangle {
+
+    public static int TrinomialValue(int n, int k) {
+        if (n == 0 && k == 0) {
+            return 1;
+        }
+
+        if (k < -n || k > n) {
+            return 0;
+        }
+
+        return TrinomialValue(n - 1, k - 1) + TrinomialValue(n - 1, k) + TrinomialValue(n - 1, k + 1);
+    }
+
+    public static void printTrinomial(int n) {
+        for (int i = 0; i < n; i++) {
+            for (int j = -i; j <= 0; j++) {
+                System.out.print(TrinomialValue(i, j) + " ");
+            }
+
+            for (int j = 1; j <= i; j++) {
+                System.out.print(TrinomialValue(i, j) + " ");
+            }
+
+            System.out.println();
+        }
+    }
+
+    public static void main(String argc[]) {
+        int n = 6;
+        printTrinomial(n);
+    }
+}