Rounding the solutions of Fibonacci-like difference equations Public Deposited

http://ir.library.oregonstate.edu/concern/technical_reports/g732db38m

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  • It is well known that the Fibonacci numbers can be expressed in the form Round {1/√5 λ₀[superscript n]} where λ₀ = (1 + √5)/2. [Knu75] We look at integer sequences which are solutions to non-negative difference equations and show that if the equation is 1-Bounded then the solution can be expressed as Round {αλ₀[superscript n]} where α is a constant and λ₀ is the unique positive real root of the characteristic polynomial. We also give an easy to test sufficient condition which uses monotonicity of the coefficients of the polynomial and one evaluation of the polynomial at an integer point. We use our theorems to show that the generalized Fibonacci numbers [Mil60] can be expressed in this rounded form.
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  • description.provenance : Submitted by Laura Wilson (laura.wilson@oregonstate.edu) on 2012-02-27T23:33:02Z No. of bitstreams: 1 Rounding the solutions of Fibonacci-like difference equations.pdf: 192963 bytes, checksum: 31aa5e4dba12f22812273fc8744ad1a8 (MD5)
  • description.provenance : Made available in DSpace on 2012-02-27T23:34:10Z (GMT). No. of bitstreams: 1 Rounding the solutions of Fibonacci-like difference equations.pdf: 192963 bytes, checksum: 31aa5e4dba12f22812273fc8744ad1a8 (MD5) Previous issue date: 2002-05
  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2012-02-27T23:34:09Z (GMT) No. of bitstreams: 1 Rounding the solutions of Fibonacci-like difference equations.pdf: 192963 bytes, checksum: 31aa5e4dba12f22812273fc8744ad1a8 (MD5)

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