local fmt = require "fmt"
require "table2"

local function forward_diff(a, order)
    assert(order >= 0 and order % 1 == 0, "Order must be a non-negative integer.")
    if #a == 0 then return end
    io.write(" 0: ")
    fmt.tprint("%5d", a)
    if #a == 1 then return end
    if order == 0 then return end
    for o = 1, order do
        local b = table.rep(#a - 1, 0)
        for i = 1, #b do b[i] = a[i + 1] - a[i] end
        io.write($" {o}: ")
        fmt.tprint("%5d", b)
        if #b == 1 then return end
        a = b
    end
end

forward_diff({90, 47, 58, 29, 22, 32, 55, 5, 55, 73}, 9)