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- W159323873 abstract "Continued fractions are linked to Stern's diatomic sequence 0,1,1,2,1,3,2,3,1,4,... (given by the recursion relation A_2n=A_n and A_{2n+1} = a_n + a_{n+1}, where A_0=0 and A_1=1), which has long been known. Using a particular multi-dimensional continued fraction algorithm (the Farey algorithm), we will generalize the diatomic sequence to a collection of numbers that quite naturally should be called the tri-atomic sequence (or a two-dimensional Pascal with memory sequence). As continued fractions and the diatomic sequence can be thought of as coming from systematic subdivisions of the unit interval, this new tri-atomic sequence will arise by a systematic subdivision of a triangle. We will discuss some of the algebraic properties for the tri-atomic sequence." @default.
- W159323873 created "2016-06-24" @default.
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- W159323873 date "2012-06-28" @default.
- W159323873 modified "2023-09-27" @default.
- W159323873 title "A Stern Tri-atomic sequence (Pascal's Pyramid with Memory) for a Multi-dimensional Continued Fraction Algorithm" @default.
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