On the positivity set of a linear recurrence sequence
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We consider real sequences (f n ) that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive dominating characteristic root, we establish that the density is positive. Furthermore, we determine the values that can occur as density of such a positivity set, both for the special case just mentioned and in general.
KeywordsRational Number Characteristic Root Real Sequence Positive Density Linear Recurrence
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- J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, 1957.Google Scholar