The dying rabbit problem revisited
Number Theory
2007-10-12 v1
Abstract
In this paper we study a generalization of the Fibonacci sequence in which rabbits are mortal and take more that two months to become mature. In particular we give a general recurrence relation for these sequences (improving the work in the paper Hoggatt, V. E., Jr.; Lind, D. A. "The dying rabbit problem". Fibonacci Quart. 7 1969 no. 5, 482--487) and we calculate explicitly their general term (extending the work in the paper Miles, E. P., Jr. Generalized Fibonacci numbers and associated matrices. Amer. Math. Monthly 67 1960 745--752). In passing, and as a technical requirement, we also study the behavior of the positive real roots of the characteristic polynomial of the considered sequences.
Cite
@article{arxiv.0710.2216,
title = {The dying rabbit problem revisited},
author = {Antonio M. Oller},
journal= {arXiv preprint arXiv:0710.2216},
year = {2007}
}
Comments
8 pages, submitted to ANTS-VIII