Add several elixir solutions

elixir/lucas-numbers/lib/lucas_numbers.ex

@@ -0,0 +1,18 @@
+defmodule LucasNumbers do
+  defguardp is_positive(k) when is_integer(k) and k > 0
+  @moduledoc """
+  Lucas numbers are an infinite sequence of numbers which build progressively
+  which hold a strong correlation to the golden ratio (φ or ϕ)
+
+  E.g.: 2, 1, 3, 4, 7, 11, 18, 29, ...
+  """
+  def generate(1), do: [2]
+  def generate(2), do: [2, 1]
+  def generate(count) when is_positive(count) do
+    Stream.iterate({2,1}, fn {x,y} -> {y, x+y} end)
+    |> Stream.map(fn {x,_} -> x end) 
+    |> Enum.take(count)
+  end
+
+  def generate(_), do: raise ArgumentError, "count must be specified as an integer >= 1"
+end