Fibonacci Number methods done in Lua. First two methods calculates the Fibonacci number (n), while the last method prints the Fibonacci number sequence 'n' times.

fibonacci.lua

-- Recursive Method calculating Fibonacci Number for n
function fibRecursion(n)
  if n == 0 then
		return 0
	elseif n == 1 then
		return 1
	else
		return fibRecursion(n-1) + fibRecursion(n-2)
	end
end

-- Method containing a Loop that caluclates Fibonacci Number for n
function fibLoop(n)
	if n == 0 then
		return 0
	elseif n == 1 or n == 2 then
		return 1
	else
		local fib1, fib2, fib = 1, 1, 1
		for i = 3,n do
			fib = fib1 + fib2
			fib1 = fib2
			fib2 = fib
		end
		return fib
	end
end

-- Method that prints Fibonacci Number sequence n times
function fibSequence(n)
	if(n < 0) then
		return "Parameter must be a positive number"
	else
		local results = ""
		for i = 0,n-1 do -- First number is 0
			if i == n-1 then
				results = results..fibRecursion(i) --No comma is added if last number
			else
				results = results..fibRecursion(i)..", "
			end
		end
		return "Fibonacci Sequence of the first "..n.." numbers is "..results
	end
end

-- Test Section
print("Recurssion; fib(10): "..fibRecursion(10)) -- 55
print("Loop; fib(10): "..fibLoop(10)) -- 55
print(fibSequence(10)) -- Fibonacci Sequence of the first 10 numbers is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34