SPOILER D: - - - - - - - - - - - - - - - - - - - - - - - - - - -

Solution 1:  Fibonacci numbers

  a(0) = a(1) = 1
  a(n) = a(n-1) + a(n-2)   for n >= 2

  1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...


Reference:

- Ian Stewart
  Mathematische Unterhaltungen
  Spektrum der Wissenschaften, Nov. 1995, 10-12
  (Echte oder falsche Fibonacci-Folge?. 11 Series)
  (Cites: Linderholm's rule)