A family of meta-Fibonacci sequences defined by variable order recursions

Abstract

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).

19 pages, this version includes a correction to Corollary 2.15