-- returns number of partitions of n
on partitions(n, res_table)
    if n < 2 then return 1
    if voidP(res_table) then
        res_table = []
        res_table[n] = 0
    else if res_table[n] then
        return res_table[n]
    end if
    res = 0
    i = 0
    param = 1
    repeat while param <= n
        if i mod 4 < 2 then
            res = res + partitions(n - param, res_table)
        else
            res = res - partitions(n - param, res_table)
        end if
        if i mod 2 then
            param = param + i + 2
        else
            param = param + i / 2 + 1
        end if
        i = i + 1
    end repeat
    res_table[n] = res
    return res
end