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Piecewise linear recurrence relations

Published online by Cambridge University Press:  01 August 2016

Mike Crampin
Mike Crampin*
Affiliation:
The Open University, Milton Keynes MK7 6AA
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Extract

The properties of linear, homogeneous, constant coefficient, second order recurrence relations such as

are well known. Consider however the recurrence relation

Such things are rarely studied; it may not be obvious that equation (2) generates a sequence which is periodic with period 9, which is to say that for any initial values x0, x1, the sequence x0, x1, x2, x3, … satisfies xn+9 = xn for every n. This article records some discoveries which resulted from an attempt to understand this interesting fact. These discoveries open up a field for exciting, elementary, but by no means trivial, investigations.

Type
Research Article
Information
The Mathematical Gazette , Volume 76 , Issue 477 , November 1992 , pp. 355 - 359
Copyright
Copyright © The Mathematical Association 1992

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