A family of meta-Fibonacci sequences defined by variable order   recursions
  We define a family of meta-Fibonacci sequences where the order of the of recursion at stage n is a variable r(n), and the n^{th} term of a sequence is the sum of the previous r(n) terms. For the terms of any such sequence, we give upper and lower bounds which depend only on r(n). 
Nathaniel D. Emerson