Monkey pick a banana can pick 1 or 2, a total of 50, ask how many kinds of pick-up method?

The problem comes from knowing
When I finished the discovery, the knowledge is better than I write, I am crying!!!
When I'm done, I find out that it's not what it is. The function, when affixed to the LUA code n is very large, the estimate is not resistant, the code needs to be optimized.

function banana (n)    local c = 1;    if n = = 0 Then        return 0    ElseIf n = 1 then        return 1    elseif n = 2 then        return 2    end    return (BA Nana (n-1) + banana (n-2)) * C;endfor i = 1,  ten do    print (banana (i)) end

Optimized code:

Local know = {}function banana (n)    if know[n] then        return know[n]    end    local c = 1;    if n = = 0 Then        know[n] = 0        return 0    elseif n = = 1 then        know[n] = 1        return 1    elseif n = 2 Then
   know[n] = 2        return 2    end    Local r = (banana (n-1) + banana (n-2)) * C;    Know[n] = R    return rendfor i = 1, do    print (I, banana (i)) end

Monkey pick a banana can pick 1 or 2, a total of 50, ask how many kinds of pick-up method?