Problem Statement

It is defined like the Fibonacci sequence, but whereas the next term in the Fibonacci sequence is the sum of the previous two terms, in the Q sequence the previous two terms tell you how far to go back in the Q sequence to find the two numbers to sum to make the next term of the sequence.

(This point is to ensure that caching and/or recursion limits, if it is a concern, is correctly handled).

Let's start with the solution:

Print "First 10 terms of Q = " ;
For i = 1 To 10 : Print FUNC(_q(i));" "; : Next : Print
Print "256th term = ";FUNC(_q(256))

End

_q Param(1)
  Local(2)

  If a@ < 3 Then Return (1)
  If a@ = 3 Then Return (2)

  @(0) = 1 : @(1) = 1 : @(2) = 2
  c@ = 0

  For b@ = 3 To a@-1
    @(b@) = @(b@ - @(b@-1)) + @(b@ - @(b@-2))
    If @(b@) < @(b@-1) Then c@ = c@ + 1
  Next

Return (@(a@-1))