link lists
link math

procedure main()
   local sequence, order, sol, i, original, initials, c

   original := []

   while put(original, integer(read()))

   sequence := copy(original)

   order := 0

   until c := constant(sequence) do {
      sequence := delta(sequence)
      order +:= 1
      if *sequence = 0 then
         stop("No recurrence relation found")
      }

   if c > 0 then order +:= 1

   initials := original[1+:order]

   sol := []

   every i := 1 to order do
      put(sol, (-1 ^ (i + 1)) * binocoef(order, i))

   write("recurrence of order ", order)
   write("coefficients: ", limage(sol))
   write("initial values: ", limage(initials))

end

procedure delta(seq)
   local deltaseq, i

   deltaseq := []

   every i := 2 to *seq do
      put(deltaseq, seq[i] - seq[i - 1])

   return deltaseq

end

procedure constant(seq)
   local c

   c := seq[1]

   if !seq ~= c then fail
   else return c

end