The dying rabbit problem revisited

• Published in 2007
• Added on 2015-02-18

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.

Links

• http://arxiv.org/abs/0710.2216
• http://arxiv.org/pdf/0710.2216v1

Other information

BibTeX entry

@article{Oller2007,
	key = {Oller2007},
	type = {article},
	title = {The dying rabbit problem revisited},
	author = {Oller, Antonio M.},
	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.},
	comment = {},
	date_added = {2015-02-18},
	date_published = {2007-10-01},
	urls = {http://arxiv.org/abs/0710.2216,http://arxiv.org/pdf/0710.2216v1},
	collections = {Easily explained,Animals,Fibonaccinalia},
	month = {oct},
	pages = 8,
	url = {http://arxiv.org/abs/0710.2216 http://arxiv.org/pdf/0710.2216v1},
	year = 2007,
	archivePrefix = {arXiv},
	eprint = {0710.2216},
	primaryClass = {math.NT},
	urldate = {2015-02-18}
}