A family of meta-Fibonacci sequences defined by variable order recursions
Combinatorics
2007-05-23 v2 Number Theory
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).
Keywords
Cite
@article{arxiv.math/0508522,
title = {A family of meta-Fibonacci sequences defined by variable order recursions},
author = {Nathaniel D. Emerson},
journal= {arXiv preprint arXiv:math/0508522},
year = {2007}
}
Comments
19 pages, this version includes a correction to Corollary 2.15