Integer#super_catalan?: Add

lib/numb/super_catalan.rb

@@ -0,0 +1,17 @@
+# coding: utf-8
+class Integer
+  def super_catalan
+    n = self
+    return 1 if n <= 2
+    Rational(
+      3 * ((2 * n) - 3) * (n - 1).super_catalan - (n - 3) * (n - 2).super_catalan,
+      n
+    ).to_i
+  end
+
+  memoize :super_catalan
+
+  def super_catalan?
+    in_sequence?(seq: :super_catalan)
+  end
+end

spec/numb/super_catalan_spec.rb

@@ -0,0 +1,29 @@
+# coding: utf-8
+# A001003 
+SUPER_CATALAN = [1,1,3,11,45,197,903,4279,20793,103049,518859,
+                 2646723,13648869,71039373,372693519,1968801519,
+                 10463578353,55909013009,300159426963,
+                 1618362158587,8759309660445,47574827600981,
+                 259215937709463,1416461675464871]
+
+describe Integer, "#super_catalan" do
+  SUPER_CATALAN.to_enum.with_index(1).each do |s, n|
+    it "returns #{s} as the #{n}#{n.ordinal} super-Catalan number" do
+      n.super_catalan.should == s
+    end
+  end
+end
+
+describe Integer, "#super_catalan?" do
+  SUPER_CATALAN.each do |n|
+    it "returns true for super-Catalan number #{n}" do
+      n.should be_super_catalan
+    end
+  end
+
+  SUPER_CATALAN.to_seq.invert.sample(100).each do |n|
+    it "returns false for non-super-Catalan number #{n}" do
+      n.should_not be_super_catalan
+    end
+  end
+end